From: Martin Kronbichler <kronbichler@lnm.mw.tum.de>
Date: Fri, 8 Apr 2016 15:21:18 +0000 (+0200)
Subject: Change many tests to use equidistant points rather than GL points
X-Git-Tag: v8.5.0-rc1~1119^2~1
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a85e275e67de80efb5c0b62fc9347ff82046a86b;p=dealii.git

Change many tests to use equidistant points rather than GL points
---

diff --git a/tests/aniso/fe_tools.cc b/tests/aniso/fe_tools.cc
index 834a2da013..5b150d4aa5 100644
--- a/tests/aniso/fe_tools.cc
+++ b/tests/aniso/fe_tools.cc
@@ -28,6 +28,7 @@
 #include <deal.II/fe/fe_dgp.h>
 #include <deal.II/fe/fe_raviart_thomas.h>
 #include <deal.II/fe/fe_system.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <deal.II/fe/fe_tools.h>
 
@@ -125,8 +126,8 @@ void test_projection (std::ostream &out)
   FE_DGQ<dim> q0(0);
   FE_DGQ<dim> q1(1);
   FE_DGQ<dim> q2(2);
-  FE_DGQ<dim> q3(3);
-  FE_DGQ<dim> q4(4);
+  FE_DGQArbitraryNodes<dim> q3(QIterated<1>(QTrapez<1>(),3));
+  FE_DGQArbitraryNodes<dim> q4(QIterated<1>(QTrapez<1>(),4));
 
   FE_DGP<dim> p0(0);
   FE_DGP<dim> p1(1);
diff --git a/tests/bits/error_estimator_01.cc b/tests/bits/error_estimator_01.cc
index 1fa0fda70d..8db504e824 100644
--- a/tests/bits/error_estimator_01.cc
+++ b/tests/bits/error_estimator_01.cc
@@ -130,7 +130,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/error_estimator_02.cc b/tests/bits/error_estimator_02.cc
index fd7bd09dc3..b93da46853 100644
--- a/tests/bits/error_estimator_02.cc
+++ b/tests/bits/error_estimator_02.cc
@@ -130,7 +130,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/mapping_q_eulerian_06.cc b/tests/bits/mapping_q_eulerian_06.cc
index 2a75c8e19b..1a2c1470d8 100644
--- a/tests/bits/mapping_q_eulerian_06.cc
+++ b/tests/bits/mapping_q_eulerian_06.cc
@@ -44,7 +44,7 @@ void test(unsigned int degree)
   const unsigned int spacedim = 1;
   Triangulation<dim, spacedim> tria;
   GridGenerator::hyper_cube(tria, 0, 1);
-  FE_Q<dim, spacedim> fe(degree);
+  FE_Q<dim, spacedim> fe(QIterated<1>(QTrapez<1>(),degree));
 
   DoFHandler<dim, spacedim> shift_dh(tria);
 
@@ -87,4 +87,3 @@ int main ()
   test(3);
   return 0;
 }
-
diff --git a/tests/bits/point_difference_01.cc b/tests/bits/point_difference_01.cc
index b74b69b163..0072e23ec1 100644
--- a/tests/bits/point_difference_01.cc
+++ b/tests/bits/point_difference_01.cc
@@ -110,7 +110,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/point_difference_02.cc b/tests/bits/point_difference_02.cc
index b6d8ebf93c..c6038e3df5 100644
--- a/tests/bits/point_difference_02.cc
+++ b/tests/bits/point_difference_02.cc
@@ -115,7 +115,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/point_gradient_01.cc b/tests/bits/point_gradient_01.cc
index 92617096e7..ef00440d5f 100644
--- a/tests/bits/point_gradient_01.cc
+++ b/tests/bits/point_gradient_01.cc
@@ -138,7 +138,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/point_gradient_02.cc b/tests/bits/point_gradient_02.cc
index e403484113..81b4eaa3d8 100644
--- a/tests/bits/point_gradient_02.cc
+++ b/tests/bits/point_gradient_02.cc
@@ -139,7 +139,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   MappingQGeneric<dim> mapping(1);
   dof.distribute_dofs(element);
diff --git a/tests/bits/point_gradient_hp_01.cc b/tests/bits/point_gradient_hp_01.cc
index dac0ee3da1..2a812aad78 100644
--- a/tests/bits/point_gradient_hp_01.cc
+++ b/tests/bits/point_gradient_hp_01.cc
@@ -140,9 +140,9 @@ check ()
   make_mesh (tria);
 
   hp::FECollection<dim> fe;
-  fe.push_back (FE_Q<dim>(3));
-  fe.push_back (FE_Q<dim>(4));
-  fe.push_back (FE_Q<dim>(5));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),5)));
 
   hp::DoFHandler<dim> dof_handler (tria);
 
diff --git a/tests/bits/point_gradient_hp_02.cc b/tests/bits/point_gradient_hp_02.cc
index 1e2e577f2a..14aa1c18cd 100644
--- a/tests/bits/point_gradient_hp_02.cc
+++ b/tests/bits/point_gradient_hp_02.cc
@@ -141,9 +141,9 @@ check ()
   make_mesh (tria);
 
   hp::FECollection<dim> fe;
-  fe.push_back (FE_Q<dim>(3));
-  fe.push_back (FE_Q<dim>(4));
-  fe.push_back (FE_Q<dim>(5));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),5)));
 
   hp::MappingCollection<dim> mapping_1;
   mapping_1.push_back(MappingQGeneric<dim>(1));
diff --git a/tests/bits/point_value_01.cc b/tests/bits/point_value_01.cc
index 46f0b815b4..0dc3b50996 100644
--- a/tests/bits/point_value_01.cc
+++ b/tests/bits/point_value_01.cc
@@ -109,7 +109,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   dof.distribute_dofs(element);
 
diff --git a/tests/bits/point_value_02.cc b/tests/bits/point_value_02.cc
index daf1bfebc8..c4b16212c1 100644
--- a/tests/bits/point_value_02.cc
+++ b/tests/bits/point_value_02.cc
@@ -110,7 +110,7 @@ check ()
   Triangulation<dim> tria;
   make_mesh (tria);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tria);
   MappingQGeneric<dim> mapping(1);
   dof.distribute_dofs(element);
diff --git a/tests/codim_one/error_estimator_01.cc b/tests/codim_one/error_estimator_01.cc
index 743b06ee63..b260cc9d31 100644
--- a/tests/codim_one/error_estimator_01.cc
+++ b/tests/codim_one/error_estimator_01.cc
@@ -128,7 +128,7 @@ check ()
   Triangulation<dim,spacedim> tria;
   make_mesh (tria);
 
-  FE_Q<dim,spacedim> element(3);
+  FE_Q<dim,spacedim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim,spacedim> dof(tria);
   dof.distribute_dofs(element);
 
@@ -202,7 +202,7 @@ check ()
 int main ()
 {
   std::ofstream logfile ("output");
-  deallog << std::setprecision (4);
+  deallog << std::setprecision (2);
   deallog << std::fixed;
   deallog.attach(logfile);
 
diff --git a/tests/codim_one/gradients_1.cc b/tests/codim_one/gradients_1.cc
index 02af50856b..06eb8036e7 100644
--- a/tests/codim_one/gradients_1.cc
+++ b/tests/codim_one/gradients_1.cc
@@ -63,7 +63,7 @@ void test(std::string filename, unsigned int degree = 1)
 
   // finite elements used for the
   // projection
-  const FE_Q<dim,spacedim> fe (degree);
+  const FE_Q<dim,spacedim> fe (QIterated<1>(QTrapez<1>(),degree));
   const MappingQ<dim, spacedim> mapping(degree);
 
   DoFHandler<dim,spacedim> dof_handler (triangulation);
@@ -133,4 +133,3 @@ int main ()
 
   return 0;
 }
-
diff --git a/tests/fe/derivatives.cc b/tests/fe/derivatives.cc
index 55ab294738..e3ab65ee09 100644
--- a/tests/fe/derivatives.cc
+++ b/tests/fe/derivatives.cc
@@ -88,10 +88,10 @@ void plot_FE_Q_shape_functions()
   FE_Q<dim> q2(2);
   plot_derivatives(m, q2, "Q2");
 //  plot_face_shape_functions(m, q2, "Q2");
-  FE_Q<dim> q3(3);
+  FE_Q<dim> q3(QIterated<1>(QTrapez<1>(),3));
   plot_derivatives(m, q3, "Q3");
 //  plot_face_shape_functions(m, q3, "Q3");
-  FE_Q<dim> q4(4);
+  FE_Q<dim> q4(QIterated<1>(QTrapez<1>(),4));
   plot_derivatives(m, q4, "Q4");
 //  plot_face_shape_functions(m, q4, "Q4");
 //    FE_Q<dim> q5(5);
@@ -119,10 +119,10 @@ void plot_FE_DGQ_shape_functions()
   FE_DGQ<dim> q2(2);
   plot_derivatives(m, q2, "DGQ2");
 //  plot_face_shape_functions(m, q2, "DGQ2");
-  FE_DGQ<dim> q3(3);
+  FE_DGQArbitraryNodes<dim> q3(QIterated<1>(QTrapez<1>(),3));
   plot_derivatives(m, q3, "DGQ3");
 //  plot_face_shape_functions(m, q3, "DGQ3");
-  FE_DGQ<dim> q4(4);
+  FE_DGQArbitraryNodes<dim> q4(QIterated<1>(QTrapez<1>(),4));
   plot_derivatives(m, q4, "DGQ4");
 //  plot_face_shape_functions(m, q4, "DGQ4");
 //    FE_DGQ<dim> q5(5);
@@ -165,7 +165,7 @@ main()
   // FESystem test.
   MappingQGeneric<2> m(1);
   FESystem<2> q2_q3(FE_Q<2>(2), 1,
-                    FE_Q<2>(3), 1);
+                    FE_Q<2>(QIterated<1>(QTrapez<1>(),3)), 1);
 //  plot_derivatives(m, q2_q3, "Q2_Q3");
 
   return 0;
diff --git a/tests/fe/fe_prolongation_sys_04.cc b/tests/fe/fe_prolongation_sys_04.cc
index 3d9e534d9b..eac3b3be29 100644
--- a/tests/fe/fe_prolongation_sys_04.cc
+++ b/tests/fe/fe_prolongation_sys_04.cc
@@ -25,5 +25,5 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(3),3,2);
+  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(QIterated<1>(QTrapez<1>(),3)),3,2);
 }
diff --git a/tests/fe/fe_prolongation_sys_05.cc b/tests/fe/fe_prolongation_sys_05.cc
index 9a508790ba..95fb4f6fab 100644
--- a/tests/fe/fe_prolongation_sys_05.cc
+++ b/tests/fe/fe_prolongation_sys_05.cc
@@ -26,7 +26,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3((FESystem<2>(FE_Q<2>(1),3)), 3,
-             FE_DGQ<2>(3), 1,
+             FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
              FE_Q<2>(1), 3,
              2);
 }
diff --git a/tests/fe/fe_prolongation_sys_06.cc b/tests/fe/fe_prolongation_sys_06.cc
index b86d958c7b..7603ab4a1f 100644
--- a/tests/fe/fe_prolongation_sys_06.cc
+++ b/tests/fe/fe_prolongation_sys_06.cc
@@ -25,8 +25,8 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(3), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
+  CHECK_SYS3(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
              FESystem<2>(FE_Q<2>(2),3,
                          FE_DGQ<2>(0),1),2,
              2);
diff --git a/tests/fe/fe_prolongation_sys_08.cc b/tests/fe/fe_prolongation_sys_08.cc
index 50fde1cc6e..6b944d575b 100644
--- a/tests/fe/fe_prolongation_sys_08.cc
+++ b/tests/fe/fe_prolongation_sys_08.cc
@@ -26,7 +26,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3(FE_Nedelec<2>(0), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
              FESystem<2>(FE_Q<2>(2),3,
                          FE_Nedelec<2>(0),2),2,
              2);
diff --git a/tests/fe/fe_prolongation_sys_09.cc b/tests/fe/fe_prolongation_sys_09.cc
index 52a4f68bd6..d31375caef 100644
--- a/tests/fe/fe_prolongation_sys_09.cc
+++ b/tests/fe/fe_prolongation_sys_09.cc
@@ -25,7 +25,7 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS2 (FE_DGQ<2>(3), 1,
+  CHECK_SYS2 (FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
               FE_Nedelec<2>(1), 2,
               2);
 }
diff --git a/tests/fe/fe_restriction_sys_04.cc b/tests/fe/fe_restriction_sys_04.cc
index 0ec770b93e..deabda2707 100644
--- a/tests/fe/fe_restriction_sys_04.cc
+++ b/tests/fe/fe_restriction_sys_04.cc
@@ -25,5 +25,5 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(3),3,2);
+  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(QIterated<1>(QTrapez<1>(),3)),3,2);
 }
diff --git a/tests/fe/fe_restriction_sys_05.cc b/tests/fe/fe_restriction_sys_05.cc
index 3edc85ffbf..fa9b8e9843 100644
--- a/tests/fe/fe_restriction_sys_05.cc
+++ b/tests/fe/fe_restriction_sys_05.cc
@@ -26,7 +26,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3((FESystem<2>(FE_Q<2>(1),3)), 3,
-             FE_DGQ<2>(3), 1,
+             FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
              FE_Q<2>(1), 3,
              2);
 }
diff --git a/tests/fe/fe_restriction_sys_06.cc b/tests/fe/fe_restriction_sys_06.cc
index 0b9d7544f2..6c2be409c7 100644
--- a/tests/fe/fe_restriction_sys_06.cc
+++ b/tests/fe/fe_restriction_sys_06.cc
@@ -25,8 +25,8 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(3), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
+  CHECK_SYS3(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
              FESystem<2>(FE_Q<2>(2),3,
                          FE_DGQ<2>(0),1),2,
              2);
diff --git a/tests/fe/fe_restriction_sys_07.cc b/tests/fe/fe_restriction_sys_07.cc
index c254b8270c..eb9c8173d5 100644
--- a/tests/fe/fe_restriction_sys_07.cc
+++ b/tests/fe/fe_restriction_sys_07.cc
@@ -25,7 +25,7 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS2 (FE_DGQ<2>(3), 1,
+  CHECK_SYS2 (FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
               FE_Nedelec<2>(0), 2,
               2);
 }
diff --git a/tests/fe/fe_restriction_sys_08.cc b/tests/fe/fe_restriction_sys_08.cc
index 701744203b..ca5a249947 100644
--- a/tests/fe/fe_restriction_sys_08.cc
+++ b/tests/fe/fe_restriction_sys_08.cc
@@ -26,7 +26,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3(FE_Nedelec<2>(0), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
              FESystem<2>(FE_Q<2>(2),3,
                          FE_Nedelec<2>(0),2),2,
              2);
diff --git a/tests/fe/fe_restriction_sys_09.cc b/tests/fe/fe_restriction_sys_09.cc
index 4ae768b83f..96df13f775 100644
--- a/tests/fe/fe_restriction_sys_09.cc
+++ b/tests/fe/fe_restriction_sys_09.cc
@@ -25,7 +25,7 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS2 (FE_DGQ<2>(3), 1,
+  CHECK_SYS2 (FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
               FE_Nedelec<2>(1), 2,
               2);
 }
diff --git a/tests/fe/fe_restriction_sys_10.cc b/tests/fe/fe_restriction_sys_10.cc
index 7ac6b0b407..9e978650e7 100644
--- a/tests/fe/fe_restriction_sys_10.cc
+++ b/tests/fe/fe_restriction_sys_10.cc
@@ -25,7 +25,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3(FE_Nedelec<2>(1), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
              FESystem<2>(FE_Q<2>(2),3,
                          FE_Nedelec<2>(1),2),2,
              2);
diff --git a/tests/fe/fe_support_points_sys_04.cc b/tests/fe/fe_support_points_sys_04.cc
index ae6c7364e2..00b161ab6c 100644
--- a/tests/fe/fe_support_points_sys_04.cc
+++ b/tests/fe/fe_support_points_sys_04.cc
@@ -25,5 +25,5 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(3),3,2);
+  CHECK_SYS3(FE_DGQ<2>(2),2,FE_DGQ<2>(2),2,FE_Q<2>(QIterated<1>(QTrapez<1>(),3)),3,2);
 }
diff --git a/tests/fe/fe_support_points_sys_05.cc b/tests/fe/fe_support_points_sys_05.cc
index cb5c6ef52e..2341ec998d 100644
--- a/tests/fe/fe_support_points_sys_05.cc
+++ b/tests/fe/fe_support_points_sys_05.cc
@@ -26,7 +26,7 @@ main()
   deallog.threshold_double(1.e-10);
 
   CHECK_SYS3((FESystem<2>(FE_Q<2>(1),3)), 3,
-             FE_DGQ<2>(3), 1,
+             FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
              FE_Q<2>(1), 3,
              2);
 }
diff --git a/tests/fe/fe_support_points_sys_06.cc b/tests/fe/fe_support_points_sys_06.cc
index d32cdd5623..78df37c40a 100644
--- a/tests/fe/fe_support_points_sys_06.cc
+++ b/tests/fe/fe_support_points_sys_06.cc
@@ -25,9 +25,9 @@ main()
   initlog();
   deallog.threshold_double(1.e-10);
 
-  CHECK_SYS3(FE_DGQ<2>(3), 1,
-             FESystem<2>(FE_DGQ<2>(3),3), 1,
-             FESystem<2>(FE_Q<2>(2),3,
+  CHECK_SYS3(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)), 1,
+             FESystem<2>(FE_DGQArbitraryNodes<2>(QIterated<1>(QTrapez<1>(),3)),3), 1,
+             FESystem<2>(FE_Q<2>(QIterated<1>(QTrapez<1>(),2)),3,
                          FE_DGQ<2>(0),1),2,
              2);
 }
diff --git a/tests/fe/fe_values_view_01.cc b/tests/fe/fe_values_view_01.cc
index aefce3148b..54693ec65e 100644
--- a/tests/fe/fe_values_view_01.cc
+++ b/tests/fe/fe_values_view_01.cc
@@ -99,7 +99,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_02.cc b/tests/fe/fe_values_view_02.cc
index e0e93d372e..5ef900daa1 100644
--- a/tests/fe/fe_values_view_02.cc
+++ b/tests/fe/fe_values_view_02.cc
@@ -124,7 +124,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_05.cc b/tests/fe/fe_values_view_05.cc
index 71abeedea0..9a4987d042 100644
--- a/tests/fe/fe_values_view_05.cc
+++ b/tests/fe/fe_values_view_05.cc
@@ -91,7 +91,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_07.cc b/tests/fe/fe_values_view_07.cc
index 1b5cc7d985..e74dd412ad 100644
--- a/tests/fe/fe_values_view_07.cc
+++ b/tests/fe/fe_values_view_07.cc
@@ -92,7 +92,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_11.cc b/tests/fe/fe_values_view_11.cc
index 21fdd4c161..59edd51a1a 100644
--- a/tests/fe/fe_values_view_11.cc
+++ b/tests/fe/fe_values_view_11.cc
@@ -97,7 +97,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_13.cc b/tests/fe/fe_values_view_13.cc
index cd105c0953..459bdf0238 100644
--- a/tests/fe/fe_values_view_13.cc
+++ b/tests/fe/fe_values_view_13.cc
@@ -98,7 +98,7 @@ void test_hyper_sphere()
 
   FESystem<dim> fe (FE_Q<dim>(1), 1,
                     FE_Q<dim>(2), 2,
-                    FE_DGQ<dim>(3), dim);
+                    FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),3)), dim);
   test(tr, fe);
 }
 
diff --git a/tests/fe/fe_values_view_30.cc b/tests/fe/fe_values_view_30.cc
index 3c6f6c0197..d7d069b92f 100644
--- a/tests/fe/fe_values_view_30.cc
+++ b/tests/fe/fe_values_view_30.cc
@@ -170,7 +170,7 @@ void test_hyper_sphere()
 
   const unsigned int order = 3;
 
-  test(tr, FESystem<dim> (FE_Q<dim>(order), dim) );
+  test(tr, FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),order)), dim) );
 }
 
 
diff --git a/tests/fe/injection_dgq.cc b/tests/fe/injection_dgq.cc
index 3dcbb52d24..cd6ab82b1d 100644
--- a/tests/fe/injection_dgq.cc
+++ b/tests/fe/injection_dgq.cc
@@ -17,6 +17,7 @@
 
 char logname[] = "output";
 
+#include <deal.II/base/quadrature_lib.h>
 
 #include "injection_common.h"
 
@@ -28,5 +29,13 @@ void test ()
 
   for (unsigned int i=0; i<4; ++i)
     for (unsigned int j=i; j<4; ++j)
-      do_check (FE_DGQ<dim>(i), FE_DGQ<dim>(j));
+      if (i > 0 && j > 0)
+        do_check (FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),i)),
+                  FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),j)));
+      else if (j > 0)
+        do_check (FE_DGQ<dim>(0),
+                  FE_DGQArbitraryNodes<dim>(QIterated<1>(QTrapez<1>(),j)));
+      else
+        do_check (FE_DGQ<dim>(0),
+                  FE_DGQ<dim>(0));
 }
diff --git a/tests/fe/injection_q.cc b/tests/fe/injection_q.cc
index a6639e0cbd..ba8799a76b 100644
--- a/tests/fe/injection_q.cc
+++ b/tests/fe/injection_q.cc
@@ -17,6 +17,7 @@
 
 char logname[] = "output";
 
+#include <deal.II/base/quadrature_lib.h>
 
 #include "injection_common.h"
 
@@ -27,5 +28,6 @@ void test ()
   deallog << std::setprecision (10);
   for (unsigned int i=1; i<4; ++i)
     for (unsigned int j=i; j<4; ++j)
-      do_check (FE_Q<dim>(i), FE_Q<dim>(j));
+      do_check (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),
+                FE_Q<dim>(QIterated<1>(QTrapez<1>(),j)));
 }
diff --git a/tests/fe/injection_q_dg0.cc b/tests/fe/injection_q_dg0.cc
index 50ecae0f21..8459ec15cf 100644
--- a/tests/fe/injection_q_dg0.cc
+++ b/tests/fe/injection_q_dg0.cc
@@ -17,9 +17,11 @@
 
 char logname[] = "output";
 
+#include <deal.II/base/quadrature_lib.h>
 
 #include "injection_common.h"
 
+
 template <int dim>
 void test ()
 {
@@ -28,6 +30,7 @@ void test ()
     for (unsigned int j=i; j<4; ++j)
       {
         deallog << "inj " << i << " " << j << ":" << std::endl;
-        do_check (FE_Q_DG0<dim>(i), FE_Q_DG0<dim>(j));
+        do_check (FE_Q_DG0<dim>(QIterated<1>(QTrapez<1>(),i)),
+                  FE_Q_DG0<dim>(QIterated<1>(QTrapez<1>(),j)));
       }
 }
diff --git a/tests/fe/injection_q_system.cc b/tests/fe/injection_q_system.cc
index 5ea40e65b7..7fe7f806f3 100644
--- a/tests/fe/injection_q_system.cc
+++ b/tests/fe/injection_q_system.cc
@@ -17,6 +17,7 @@
 
 char logname[] = "output";
 
+#include <deal.II/base/quadrature_lib.h>
 
 #include "injection_common.h"
 
@@ -28,8 +29,8 @@ void test ()
 
   for (unsigned int i=1; i<4; ++i)
     for (unsigned int j=i; j<4; ++j)
-      do_check (FESystem<dim>(FE_Q<dim>(i), 1,
+      do_check (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
                               FE_DGQ<dim>(i-1), 1),
-                FESystem<dim>(FE_Q<dim>(j), 1,
+                FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),j)), 1,
                               FE_DGQ<dim>(j-1), 1));
 }
diff --git a/tests/fe/q_1.cc b/tests/fe/q_1.cc
index 5fd222ae35..61e69adf3e 100644
--- a/tests/fe/q_1.cc
+++ b/tests/fe/q_1.cc
@@ -62,26 +62,18 @@ main()
   deallog.attach(logfile);
   deallog.threshold_double(1.e-10);
 
-
-  // Test the non-equidistant version as
-  // well
-  const QGaussLobatto<1> quad(5);
-
-  // no constraints in 1d, but we had
-  // the matrices precomputed up to
-  // Q4 for 2d and Q2 for 3d
+  // no constraints in 1d, but we had the matrices precomputed up to Q4 for 2d
+  // and Q2 for 3d
   for (unsigned int degree=1; degree<=4; ++degree)
-    test<2>(FE_Q<2>(degree));
+    test<2>(FE_Q<2>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<2>(FE_Q<2>(quad));
+  // test the standard version (non-equidistant) as well
+  test<2>(FE_Q<2>(4));
 
   for (unsigned int degree=1; degree<=2; ++degree)
     test<3>(FE_Q<3>(degree));
 
-  test<3>(FE_Q<3>(quad));
+  test<3>(FE_Q<3>(4));
 
   return 0;
 }
-
-
-
diff --git a/tests/fe/q_2.cc b/tests/fe/q_2.cc
index 326c984d4b..98b65f0203 100644
--- a/tests/fe/q_2.cc
+++ b/tests/fe/q_2.cc
@@ -67,30 +67,22 @@ main()
   deallog.attach(logfile);
   deallog.threshold_double(1.e-10);
 
-  // Test the non-equidistant version as
-  // well
-  const QGaussLobatto<1> quad(5);
-
-  // we had the matrices precomputed
-  // up to Q4 for 1d, Q3 for 2d and
-  // Q2 for 3d
+  // we had the matrices precomputed up to Q4 for 1d, Q3 for 2d and Q2 for 3d
   for (unsigned int degree=1; degree<=4; ++degree)
-    test<1>(FE_Q<1>(degree));
+    test<1>(FE_Q<1>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<1>(FE_Q<1>(quad));
+  // test the standard version (non-equidistant) as well
+  test<1>(FE_Q<1>(4));
 
   for (unsigned int degree=1; degree<=3; ++degree)
-    test<2>(FE_Q<2>(degree));
+    test<2>(FE_Q<2>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<2>(FE_Q<2>(quad));
+  test<2>(FE_Q<2>(4));
 
   for (unsigned int degree=1; degree<=2; ++degree)
     test<3>(FE_Q<3>(degree));
 
-  test<3>(FE_Q<3>(quad));
+  test<3>(FE_Q<3>(4));
 
   return 0;
 }
-
-
-
diff --git a/tests/fe/q_3.cc b/tests/fe/q_3.cc
index 5f97f7bcb1..84095ebd43 100644
--- a/tests/fe/q_3.cc
+++ b/tests/fe/q_3.cc
@@ -64,29 +64,22 @@ main()
   deallog.attach(logfile);
   deallog.threshold_double(1.e-10);
 
-  // Test the non-equidistant version as
-  // well
-  const QGaussLobatto<1> quad(5);
-
-  // we had the matrices precomputed
-  // up to Q4 for 1d, 2d and 3d
+  // we had the matrices precomputed up to Q4 for 1d, 2d and 3d
   for (unsigned int degree=1; degree<=4; ++degree)
-    test<1>(FE_Q<1>(degree));
+    test<1>(FE_Q<1>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<1>(FE_Q<1>(quad));
+  // test the standard version (non-equidistant) as well
+  test<1>(FE_Q<1>(4));
 
   for (unsigned int degree=1; degree<=4; ++degree)
-    test<2>(FE_Q<2>(degree));
+    test<2>(FE_Q<2>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<2>(FE_Q<2>(quad));
+  test<2>(FE_Q<2>(4));
 
   for (unsigned int degree=1; degree<=4; ++degree)
-    test<3>(FE_Q<3>(degree));
+    test<3>(FE_Q<3>(QIterated<1>(QTrapez<1>(),degree)));
 
-  test<3>(FE_Q<3>(quad));
+  test<3>(FE_Q<3>(4));
 
   return 0;
 }
-
-
-
diff --git a/tests/fe/q_4.cc b/tests/fe/q_4.cc
index a11926a174..cd86cc2594 100644
--- a/tests/fe/q_4.cc
+++ b/tests/fe/q_4.cc
@@ -69,7 +69,8 @@ main()
 
   for (unsigned int degree1=1; degree1<=4; ++degree1)
     for (unsigned int degree2=1; degree2<=4; ++degree2)
-      test<1>(FE_Q<1>(degree1), FE_Q<1>(degree2));
+      test<1>(FE_Q<1>(QIterated<1>(QTrapez<1>(),degree1)),
+              FE_Q<1>(QIterated<1>(QTrapez<1>(),degree2)));
   for (unsigned int degree1=2; degree1<=5; ++degree1)
     for (unsigned int degree2=2; degree2<=5; ++degree2)
       test<1>(FE_Q<1>(QGaussLobatto<1>(degree1)),
@@ -77,7 +78,8 @@ main()
 
   for (unsigned int degree1=1; degree1<=3; ++degree1)
     for (unsigned int degree2=1; degree2<=3; ++degree2)
-      test<2>(FE_Q<2>(degree1), FE_Q<2>(degree2));
+      test<2>(FE_Q<2>(QIterated<1>(QTrapez<1>(),degree1)),
+              FE_Q<2>(QIterated<1>(QTrapez<1>(),degree2)));
   for (unsigned int degree1=2; degree1<=4; ++degree1)
     for (unsigned int degree2=2; degree2<=4; ++degree2)
       test<2>(FE_Q<2>(QGaussLobatto<1>(degree1)),
@@ -85,7 +87,8 @@ main()
 
   for (unsigned int degree1=1; degree1<=2; ++degree1)
     for (unsigned int degree2=1; degree2<=2; ++degree2)
-      test<3>(FE_Q<3>(degree1), FE_Q<3>(degree2));
+      test<3>(FE_Q<3>(QIterated<1>(QTrapez<1>(),degree1)),
+              FE_Q<3>(QIterated<1>(QTrapez<1>(),degree2)));
   for (unsigned int degree1=2; degree1<=4; ++degree1)
     for (unsigned int degree2=2; degree2<=4; ++degree2)
       test<3>(FE_Q<3>(QGaussLobatto<1>(degree1)),
@@ -94,6 +97,3 @@ main()
 
   return 0;
 }
-
-
-
diff --git a/tests/fe/q_bubbles_projection_01.cc b/tests/fe/q_bubbles_projection_01.cc
index d4821a4ec0..2dcb306165 100644
--- a/tests/fe/q_bubbles_projection_01.cc
+++ b/tests/fe/q_bubbles_projection_01.cc
@@ -29,6 +29,6 @@ char logname[] = "output";
 
 void test ()
 {
-  FESystem<2> fe (FE_Q_Bubbles<2>(3), 2);
+  FESystem<2> fe (FE_Q_Bubbles<2>(QIterated<1>(QTrapez<1>(),3)), 2);
   check (fe);
 }
diff --git a/tests/fe/shapes_dgq.cc b/tests/fe/shapes_dgq.cc
index 86ec292130..204f1b2233 100644
--- a/tests/fe/shapes_dgq.cc
+++ b/tests/fe/shapes_dgq.cc
@@ -39,13 +39,12 @@ void plot_FE_DGQ_shape_functions()
   plot_face_shape_functions(m, q2, "DGQ2");
   test_compute_functions(m, q2, "DGQ2");
 
-  FE_DGQ<dim> q3(3);
+  FE_DGQArbitraryNodes<dim> q3(QIterated<1>(QTrapez<1>(),3));
   plot_shape_functions(m, q3, "DGQ3");
   plot_face_shape_functions(m, q3, "DGQ3");
   test_compute_functions(m, q3, "DGQ3");
 
-  QGaussLobatto<1> quadrature_gl(5);
-  FE_DGQArbitraryNodes<dim> qgl(quadrature_gl);
+  FE_DGQ<dim> qgl(4);
   plot_shape_functions(m, qgl, "DGQGL");
   plot_face_shape_functions(m, qgl, "DGQGL");
   test_compute_functions(m, qgl, "DGQGL");
diff --git a/tests/fe/shapes_q.cc b/tests/fe/shapes_q.cc
index 4f983191c8..d76a7ebd06 100644
--- a/tests/fe/shapes_q.cc
+++ b/tests/fe/shapes_q.cc
@@ -43,12 +43,12 @@ void plot_FE_Q_shape_functions()
   // reduce run-time
   if (dim < 3)
     {
-      FE_Q<dim> q3(3);
+      FE_Q<dim> q3(QIterated<1>(QTrapez<1>(),3));
       plot_shape_functions(m, q3, "Q3");
       plot_face_shape_functions(m, q3, "Q3");
       test_compute_functions(m, q3, "Q3");
 
-      FE_Q<dim> q4(4);
+      FE_Q<dim> q4(QIterated<1>(QTrapez<1>(),4));
       plot_shape_functions(m, q4, "Q4");
       plot_face_shape_functions(m, q4, "Q4");
       test_compute_functions(m, q4, "Q4");
diff --git a/tests/fe/shapes_q_bubbles.cc b/tests/fe/shapes_q_bubbles.cc
index c82ad0bba5..90254cf5e9 100644
--- a/tests/fe/shapes_q_bubbles.cc
+++ b/tests/fe/shapes_q_bubbles.cc
@@ -44,12 +44,12 @@ void plot_FE_Q_Bubbles_shape_functions()
   // reduce run-time
   if (dim < 3)
     {
-      FE_Q_Bubbles<dim> q3(3);
+      FE_Q_Bubbles<dim> q3(QIterated<1>(QTrapez<1>(),3));
       plot_shape_functions(m, q3, "Q3_Bubbles");
       plot_face_shape_functions(m, q3, "Q3_Bubbles");
       test_compute_functions(m, q3, "Q3_Bubbles");
 
-      FE_Q_Bubbles<dim> q4(4);
+      FE_Q_Bubbles<dim> q4(QIterated<1>(QTrapez<1>(),4));
       plot_shape_functions(m, q4, "Q4_Bubbles");
       plot_face_shape_functions(m, q4, "Q4_Bubbles");
       test_compute_functions(m, q4, "Q4_Bubbles");
diff --git a/tests/fe/shapes_q_dg0.cc b/tests/fe/shapes_q_dg0.cc
index 42d001a50c..ca94ca0032 100644
--- a/tests/fe/shapes_q_dg0.cc
+++ b/tests/fe/shapes_q_dg0.cc
@@ -43,12 +43,12 @@ void plot_FE_Q_DG0_shape_functions()
   // reduce run-time
   if (dim < 3)
     {
-      FE_Q_DG0<dim> q3(3);
+      FE_Q_DG0<dim> q3(QIterated<1>(QTrapez<1>(),3));
       plot_shape_functions(m, q3, "Q3_DG0");
       plot_face_shape_functions(m, q3, "Q3_DG0");
       test_compute_functions(m, q3, "Q3_DG0");
 
-      FE_Q_DG0<dim> q4(4);
+      FE_Q_DG0<dim> q4(QIterated<1>(QTrapez<1>(),4));
       plot_shape_functions(m, q4, "Q4_DG0");
       plot_face_shape_functions(m, q4, "Q4_DG0");
       test_compute_functions(m, q4, "Q4_DG0");
diff --git a/tests/grid/mesh_3d_25.cc b/tests/grid/mesh_3d_25.cc
index e1601b5070..4c1b74be75 100644
--- a/tests/grid/mesh_3d_25.cc
+++ b/tests/grid/mesh_3d_25.cc
@@ -119,4 +119,3 @@ int main ()
   create_two_cubes_rotation(triangulation,1);
   test<3>(triangulation);
 }
-
diff --git a/tests/grid/mesh_3d_26.cc b/tests/grid/mesh_3d_26.cc
index 43279b492c..60e48f0cb0 100644
--- a/tests/grid/mesh_3d_26.cc
+++ b/tests/grid/mesh_3d_26.cc
@@ -121,4 +121,3 @@ int main ()
   triangulation.refine_global(1);
   test<3>(triangulation);
 }
-
diff --git a/tests/hp/crash_08.cc b/tests/hp/crash_08.cc
index 0a0ffd3714..8cb9a3934a 100644
--- a/tests/hp/crash_08.cc
+++ b/tests/hp/crash_08.cc
@@ -70,7 +70,7 @@ int main ()
   hp::FECollection<2> fe;
   fe.push_back (FE_Q<2>(1));
   fe.push_back (FE_Q<2>(2));
-  fe.push_back (FE_Q<2>(3));
+  fe.push_back (FE_Q<2>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<2>        dof_handler(triangulation);
 
@@ -152,4 +152,3 @@ int main ()
 
   constraints.print (deallog.get_file_stream());
 }
-
diff --git a/tests/hp/crash_09.cc b/tests/hp/crash_09.cc
index b5c7a63473..8d0e1f7b21 100644
--- a/tests/hp/crash_09.cc
+++ b/tests/hp/crash_09.cc
@@ -71,7 +71,7 @@ int main ()
   hp::FECollection<3> fe;
   fe.push_back (FE_Q<3>(1));
   fe.push_back (FE_Q<3>(2));
-  fe.push_back (FE_Q<3>(3));
+  fe.push_back (FE_Q<3>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<3>        dof_handler(triangulation);
 
@@ -144,4 +144,3 @@ done:
 
   constraints.print (deallog.get_file_stream());
 }
-
diff --git a/tests/hp/crash_10.cc b/tests/hp/crash_10.cc
index 18b422fffd..207ecde47e 100644
--- a/tests/hp/crash_10.cc
+++ b/tests/hp/crash_10.cc
@@ -30,6 +30,7 @@
 #include <deal.II/dofs/dof_accessor.h>
 
 #include <deal.II/fe/fe_q.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <deal.II/dofs/dof_tools.h>
 
@@ -46,7 +47,7 @@ void test ()
   hp::DoFHandler<dim>        dof_handler(triangulation);
   ConstraintMatrix     hanging_node_constraints;
 
-  FE_Q<dim> fe_1 (1), fe_2 (2), fe_3 (3), fe_4 (4);
+  FE_Q<dim> fe_1 (1), fe_2 (2), fe_3 (QIterated<1>(QTrapez<1>(),3)), fe_4 (QIterated<1>(QTrapez<1>(),4));
 
   fe.push_back (fe_1);
   fe.push_back (fe_2);
diff --git a/tests/hp/crash_11.cc b/tests/hp/crash_11.cc
index 291c360f86..532071f6f9 100644
--- a/tests/hp/crash_11.cc
+++ b/tests/hp/crash_11.cc
@@ -71,8 +71,8 @@ int main ()
   hp::FECollection<3> fe;
   fe.push_back (FE_Q<3>(1));
   fe.push_back (FE_Q<3>(2));
-  fe.push_back (FE_Q<3>(3));
-  fe.push_back (FE_Q<3>(4));
+  fe.push_back (FE_Q<3>(QIterated<1>(QTrapez<1>(),3)));
+  fe.push_back (FE_Q<3>(QIterated<1>(QTrapez<1>(),4)));
 
   hp::DoFHandler<3>        dof_handler(triangulation);
 
@@ -131,4 +131,3 @@ done:
 
   constraints.print (deallog.get_file_stream());
 }
-
diff --git a/tests/hp/crash_12.cc b/tests/hp/crash_12.cc
index 38b8cfd6c7..9fd6be945c 100644
--- a/tests/hp/crash_12.cc
+++ b/tests/hp/crash_12.cc
@@ -75,9 +75,9 @@ void test ()
   hp::FECollection<dim> fe;
   fe.push_back (FE_Q<dim>(1));
   fe.push_back (FE_Q<dim>(2));
-  fe.push_back (FE_Q<dim>(3));
-  fe.push_back (FE_Q<dim>(4));
-  fe.push_back (FE_Q<dim>(5));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)));
+  fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),5)));
 
   hp::DoFHandler<dim>        dof_handler(triangulation);
 
@@ -123,4 +123,3 @@ int main ()
   test<2> ();
   test<3> ();
 }
-
diff --git a/tests/hp/crash_17.cc b/tests/hp/crash_17.cc
index f765e448d5..6cd7858525 100644
--- a/tests/hp/crash_17.cc
+++ b/tests/hp/crash_17.cc
@@ -131,7 +131,7 @@ LaplaceProblem<dim>::LaplaceProblem () :
 {
   for (unsigned int degree=2; degree<5; ++degree)
     {
-      fe_collection.push_back (FE_Q<dim>(degree));
+      fe_collection.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)));
       quadrature_collection.push_back (QGauss<dim>(degree+2));
       face_quadrature_collection.push_back (QGauss<dim-1>(degree+2));
     }
diff --git a/tests/hp/crash_17_compressed_set_sparsity.cc b/tests/hp/crash_17_compressed_set_sparsity.cc
index 27d19dd88c..90b6d89795 100644
--- a/tests/hp/crash_17_compressed_set_sparsity.cc
+++ b/tests/hp/crash_17_compressed_set_sparsity.cc
@@ -133,7 +133,7 @@ LaplaceProblem<dim>::LaplaceProblem () :
 {
   for (unsigned int degree=2; degree<5; ++degree)
     {
-      fe_collection.push_back (FE_Q<dim>(degree));
+      fe_collection.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)));
       quadrature_collection.push_back (QGauss<dim>(degree+2));
       face_quadrature_collection.push_back (QGauss<dim-1>(degree+2));
     }
diff --git a/tests/hp/crash_18.cc b/tests/hp/crash_18.cc
index 71e86ea9d5..d19b78964e 100644
--- a/tests/hp/crash_18.cc
+++ b/tests/hp/crash_18.cc
@@ -134,7 +134,7 @@ LaplaceProblem<dim>::LaplaceProblem () :
 {
   for (unsigned int degree=2; degree<5; ++degree)
     {
-      fe_collection.push_back (FE_Q<dim>(degree));
+      fe_collection.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)));
       quadrature_collection.push_back (QGauss<dim>(degree+2));
       face_quadrature_collection.push_back (QGauss<dim-1>(degree+2));
     }
diff --git a/tests/hp/crash_18_compressed_set_sparsity.cc b/tests/hp/crash_18_compressed_set_sparsity.cc
index a6f29f96dd..db87cee5a4 100644
--- a/tests/hp/crash_18_compressed_set_sparsity.cc
+++ b/tests/hp/crash_18_compressed_set_sparsity.cc
@@ -137,7 +137,7 @@ LaplaceProblem<dim>::LaplaceProblem () :
 {
   for (unsigned int degree=2; degree<5; ++degree)
     {
-      fe_collection.push_back (FE_Q<dim>(degree));
+      fe_collection.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)));
       quadrature_collection.push_back (QGauss<dim>(degree+2));
       face_quadrature_collection.push_back (QGauss<dim-1>(degree+2));
     }
diff --git a/tests/hp/create_laplace_matrix_01.cc b/tests/hp/create_laplace_matrix_01.cc
index a0a081d8d3..93e60c147e 100644
--- a/tests/hp/create_laplace_matrix_01.cc
+++ b/tests/hp/create_laplace_matrix_01.cc
@@ -72,7 +72,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_01b.cc b/tests/hp/create_laplace_matrix_01b.cc
index a91c38e342..0b434dbeb1 100644
--- a/tests/hp/create_laplace_matrix_01b.cc
+++ b/tests/hp/create_laplace_matrix_01b.cc
@@ -73,7 +73,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_02.cc b/tests/hp/create_laplace_matrix_02.cc
index a77b9f6688..bc357476d0 100644
--- a/tests/hp/create_laplace_matrix_02.cc
+++ b/tests/hp/create_laplace_matrix_02.cc
@@ -72,9 +72,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_02b.cc b/tests/hp/create_laplace_matrix_02b.cc
index 23319b6eeb..951fadc82d 100644
--- a/tests/hp/create_laplace_matrix_02b.cc
+++ b/tests/hp/create_laplace_matrix_02b.cc
@@ -73,9 +73,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_03.cc b/tests/hp/create_laplace_matrix_03.cc
index 6358d72021..c02947e152 100644
--- a/tests/hp/create_laplace_matrix_03.cc
+++ b/tests/hp/create_laplace_matrix_03.cc
@@ -71,7 +71,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_03b.cc b/tests/hp/create_laplace_matrix_03b.cc
index d917fa7f25..374f0b40ac 100644
--- a/tests/hp/create_laplace_matrix_03b.cc
+++ b/tests/hp/create_laplace_matrix_03b.cc
@@ -72,7 +72,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_04.cc b/tests/hp/create_laplace_matrix_04.cc
index cebd9e42f0..e2630fff5b 100644
--- a/tests/hp/create_laplace_matrix_04.cc
+++ b/tests/hp/create_laplace_matrix_04.cc
@@ -71,9 +71,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_laplace_matrix_04b.cc b/tests/hp/create_laplace_matrix_04b.cc
index 3fd34264e9..970844ef7f 100644
--- a/tests/hp/create_laplace_matrix_04b.cc
+++ b/tests/hp/create_laplace_matrix_04b.cc
@@ -72,9 +72,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_01.cc b/tests/hp/create_mass_matrix_01.cc
index d61daa8c95..9de1d7cbbc 100644
--- a/tests/hp/create_mass_matrix_01.cc
+++ b/tests/hp/create_mass_matrix_01.cc
@@ -72,7 +72,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_01b.cc b/tests/hp/create_mass_matrix_01b.cc
index 047ff435c4..54f8a42bac 100644
--- a/tests/hp/create_mass_matrix_01b.cc
+++ b/tests/hp/create_mass_matrix_01b.cc
@@ -73,7 +73,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_02.cc b/tests/hp/create_mass_matrix_02.cc
index e11ce5261a..a9df35dcdf 100644
--- a/tests/hp/create_mass_matrix_02.cc
+++ b/tests/hp/create_mass_matrix_02.cc
@@ -72,9 +72,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_02b.cc b/tests/hp/create_mass_matrix_02b.cc
index 9a47b12a18..3ae8d86c0e 100644
--- a/tests/hp/create_mass_matrix_02b.cc
+++ b/tests/hp/create_mass_matrix_02b.cc
@@ -73,9 +73,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_03.cc b/tests/hp/create_mass_matrix_03.cc
index 69c5342357..f090c585dd 100644
--- a/tests/hp/create_mass_matrix_03.cc
+++ b/tests/hp/create_mass_matrix_03.cc
@@ -71,7 +71,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_03b.cc b/tests/hp/create_mass_matrix_03b.cc
index 0fed9b46e5..f5215463f3 100644
--- a/tests/hp/create_mass_matrix_03b.cc
+++ b/tests/hp/create_mass_matrix_03b.cc
@@ -74,7 +74,7 @@ check ()
   hp::FECollection<dim> element;
   element.push_back (FE_Q<dim>(1));
   element.push_back (FE_Q<dim>(2));
-  element.push_back (FE_Q<dim>(3));
+  element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_04.cc b/tests/hp/create_mass_matrix_04.cc
index 83743c41b8..e3443cb867 100644
--- a/tests/hp/create_mass_matrix_04.cc
+++ b/tests/hp/create_mass_matrix_04.cc
@@ -71,9 +71,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_mass_matrix_04b.cc b/tests/hp/create_mass_matrix_04b.cc
index 61ff91d0f4..0f24084f59 100644
--- a/tests/hp/create_mass_matrix_04b.cc
+++ b/tests/hp/create_mass_matrix_04b.cc
@@ -72,9 +72,9 @@ check ()
   element.push_back (FESystem<dim> (FE_Q<dim>(1), 1,
                                     FE_Q<dim>(2), 1));
   element.push_back (FESystem<dim> (FE_Q<dim>(2), 1,
-                                    FE_Q<dim>(3), 1));
-  element.push_back (FESystem<dim> (FE_Q<dim>(3), 1,
-                                    FE_Q<dim>(4), 1));
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1));
+  element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),3)), 1,
+                                    FE_Q<dim>(QIterated<1>(QTrapez<1>(),4)), 1));
 
   hp::DoFHandler<dim> dof(tr);
 
diff --git a/tests/hp/create_rhs_01.cc b/tests/hp/create_rhs_01.cc
index 3497130a7c..3a5ec144f2 100644
--- a/tests/hp/create_rhs_01.cc
+++ b/tests/hp/create_rhs_01.cc
@@ -47,7 +47,7 @@ void test ()
   triangulation.refine_global(1);
 
   //define DoFhandler and FEs
-  FE_Q<2> u(2),u2(3);
+  FE_Q<2> u(2),u2(QIterated<1>(QTrapez<1>(),3));
 
   hp::FECollection<2> fe_collection;
   fe_collection.push_back(u);
diff --git a/tests/hp/hp_constraints_q.cc b/tests/hp/hp_constraints_q.cc
index eace437386..12eaa37a30 100644
--- a/tests/hp/hp_constraints_q.cc
+++ b/tests/hp/hp_constraints_q.cc
@@ -31,7 +31,7 @@ void test ()
   std::vector<unsigned int> degrees;
   for (unsigned int i=1; i<4; ++i)
     {
-      fe.push_back (FE_Q<dim>(i));
+      fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)));
       degrees.push_back (i);
     }
 
diff --git a/tests/hp/hp_constraints_q_system.cc b/tests/hp/hp_constraints_q_system.cc
index ec77473cd9..bd74996e0b 100644
--- a/tests/hp/hp_constraints_q_system.cc
+++ b/tests/hp/hp_constraints_q_system.cc
@@ -32,7 +32,7 @@ void test ()
   std::vector<unsigned int> degrees;
   for (unsigned int i=1; i<4; ++i)
     {
-      fe.push_back (FESystem<dim>(FE_Q<dim>(i), 1,
+      fe.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
                                   FE_DGQ<dim>(i+1), 1));
       degrees.push_back (i);
     }
diff --git a/tests/hp/hp_constraints_q_system_x.cc b/tests/hp/hp_constraints_q_system_x.cc
index 565b2fa290..3b1e31dc81 100644
--- a/tests/hp/hp_constraints_q_system_x.cc
+++ b/tests/hp/hp_constraints_q_system_x.cc
@@ -34,7 +34,7 @@ void test ()
   hp::FECollection<dim> fe;
   for (unsigned int i=1; i<4; ++i)
     for (unsigned int j=0; j<4; ++j)
-      fe.push_back (FESystem<dim>(FE_Q<dim>(i), 1,
+      fe.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
                                   FE_DGQ<dim>(j), 1));
 
   deallog << "No hanging nodes test" << std::endl;
diff --git a/tests/hp/hp_hanging_nodes_01.cc b/tests/hp/hp_hanging_nodes_01.cc
index 6bb86e7b61..97670d9770 100644
--- a/tests/hp/hp_hanging_nodes_01.cc
+++ b/tests/hp/hp_hanging_nodes_01.cc
@@ -163,7 +163,7 @@ int main ()
 
   FE_Q<2> fe_1 (1);
   FE_Q<2> fe_2 (2);
-  FE_Q<2> fe_3 (3);
+  FE_Q<2> fe_3 (QIterated<1>(QTrapez<1>(),3));
 
   hp::FECollection<2> fe_coll2;
   fe_coll2.push_back (fe_3);
diff --git a/tests/hp/hp_hanging_nodes_02.cc b/tests/hp/hp_hanging_nodes_02.cc
index 1af457300f..82fc79c474 100644
--- a/tests/hp/hp_hanging_nodes_02.cc
+++ b/tests/hp/hp_hanging_nodes_02.cc
@@ -63,10 +63,10 @@ void run (bool random_p,
   hp::DoFHandler<dim>        dof_handler(triangulation);
   ConstraintMatrix     hanging_node_constraints;
 
-  FE_Q<dim> fe_1 (indx[0]),
-       fe_2 (indx[1]),
-       fe_3 (indx[2]),
-       fe_4 (indx[3]);
+  FE_Q<dim> fe_1 (QIterated<1>(QTrapez<1>(),indx[0])),
+       fe_2 (QIterated<1>(QTrapez<1>(),indx[1])),
+       fe_3 (QIterated<1>(QTrapez<1>(),indx[2])),
+       fe_4 (QIterated<1>(QTrapez<1>(),indx[3]));
 
   fe.push_back (fe_1);
   fe.push_back (fe_2);
diff --git a/tests/hp/hp_line_dof_identities_q.cc b/tests/hp/hp_line_dof_identities_q.cc
index 9c3cc579a1..f1ace27f86 100644
--- a/tests/hp/hp_line_dof_identities_q.cc
+++ b/tests/hp/hp_line_dof_identities_q.cc
@@ -22,6 +22,7 @@
 #include <deal.II/base/logstream.h>
 #include <deal.II/hp/fe_collection.h>
 #include <deal.II/fe/fe_q.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <fstream>
 
@@ -31,7 +32,7 @@ void test ()
 {
   hp::FECollection<dim> fe_collection;
   for (unsigned int i=1; i<8-dim; ++i)
-    fe_collection.push_back (FE_Q<dim>(i));
+    fe_collection.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)));
 
   for (unsigned int i=0; i<fe_collection.size(); ++i)
     for (unsigned int j=0; j<fe_collection.size(); ++j)
diff --git a/tests/hp/hp_line_dof_identities_q_system_01.cc b/tests/hp/hp_line_dof_identities_q_system_01.cc
index 02afb7d375..0c5e0779d4 100644
--- a/tests/hp/hp_line_dof_identities_q_system_01.cc
+++ b/tests/hp/hp_line_dof_identities_q_system_01.cc
@@ -23,6 +23,7 @@
 #include <deal.II/hp/fe_collection.h>
 #include <deal.II/fe/fe_q.h>
 #include <deal.II/fe/fe_system.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <fstream>
 
@@ -32,7 +33,7 @@ void test ()
 {
   hp::FECollection<dim> fe_collection;
   for (unsigned int i=1; i<8-dim; ++i)
-    fe_collection.push_back (FESystem<dim>(FE_Q<dim>(i),3));
+    fe_collection.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),3));
 
   for (unsigned int i=0; i<fe_collection.size(); ++i)
     for (unsigned int j=0; j<fe_collection.size(); ++j)
diff --git a/tests/hp/hp_line_dof_identities_q_system_02.cc b/tests/hp/hp_line_dof_identities_q_system_02.cc
index 15dafcfe90..9c6a959091 100644
--- a/tests/hp/hp_line_dof_identities_q_system_02.cc
+++ b/tests/hp/hp_line_dof_identities_q_system_02.cc
@@ -24,6 +24,7 @@
 #include <deal.II/hp/fe_collection.h>
 #include <deal.II/fe/fe_q.h>
 #include <deal.II/fe/fe_system.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <fstream>
 
@@ -37,11 +38,11 @@ void test ()
       // add the system three times, with
       // different numbers of base elements
       // and multiplicities
-      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(i),3));
-      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(i),2,
-                                             FE_Q<dim>(i),1));
-      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(i),1,
-                                             FE_Q<dim>(i),2));
+      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),3));
+      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),2,
+                                             FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),1));
+      fe_collection.push_back (FESystem<dim>(FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),1,
+                                             FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)),2));
     }
 
   for (unsigned int i=0; i<fe_collection.size(); ++i)
diff --git a/tests/hp/integrate_difference.cc b/tests/hp/integrate_difference.cc
index b1076f11cc..8d88f22cc7 100644
--- a/tests/hp/integrate_difference.cc
+++ b/tests/hp/integrate_difference.cc
@@ -56,7 +56,7 @@ void test ()
   hp::QCollection<dim> q_collection;
   for (unsigned int i=1; i<=4; ++i)
     {
-      fe_collection.push_back(FE_Q<dim> (i));
+      fe_collection.push_back(FE_Q<dim> (QIterated<1>(QTrapez<1>(),i)));
       q_collection.push_back (QGauss<dim> (i+2));
     }
 
diff --git a/tests/hp/matrices_hp.cc b/tests/hp/matrices_hp.cc
index 798ed1714f..04116f646e 100644
--- a/tests/hp/matrices_hp.cc
+++ b/tests/hp/matrices_hp.cc
@@ -143,8 +143,8 @@ check ()
   // of one Q1 and one Q2 element
   hp::FECollection<dim> element;
   for (unsigned int i=1; i<7-dim; ++i)
-    element.push_back (FESystem<dim> (FE_Q<dim>(i), 1,
-                                      FE_Q<dim>(i+1), 1));
+    element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
+                                      FE_Q<dim>(QIterated<1>(QTrapez<1>(),i+1)), 1));
   hp::DoFHandler<dim> dof(tr);
   for (typename hp::DoFHandler<dim>::active_cell_iterator
        cell = dof.begin_active(); cell!=dof.end(); ++cell)
diff --git a/tests/hp/set_dof_values_by_interpolation_03.cc b/tests/hp/set_dof_values_by_interpolation_03.cc
index fb6673ffc7..2c70b16127 100644
--- a/tests/hp/set_dof_values_by_interpolation_03.cc
+++ b/tests/hp/set_dof_values_by_interpolation_03.cc
@@ -53,7 +53,7 @@ void test ()
 
   hp::FECollection<dim> fe;
   for (unsigned int i=1; i<5; ++i)
-    fe.push_back (FE_Q<dim>(i));
+    fe.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)));
 
   hp::DoFHandler<dim> dof_handler(tr);
   for (typename hp::DoFHandler<dim>::cell_iterator cell=dof_handler.begin();
@@ -103,6 +103,3 @@ main()
 
   return 0;
 }
-
-
-
diff --git a/tests/hp/step-3b.cc b/tests/hp/step-3b.cc
index ed4093610f..256bedc42a 100644
--- a/tests/hp/step-3b.cc
+++ b/tests/hp/step-3b.cc
@@ -249,10 +249,10 @@ void LaplaceProblem::run ()
 {
   FE_Q<2> fe_1 (1),
        fe_2 (2),
-       fe_3 (3),
-       fe_4 (4),
-       fe_5 (5),
-       fe_6 (6);
+       fe_3 (QIterated<1>(QTrapez<1>(),3)),
+       fe_4 (QIterated<1>(QTrapez<1>(),4)),
+       fe_5 (QIterated<1>(QTrapez<1>(),5)),
+       fe_6 (QIterated<1>(QTrapez<1>(),6));
 
   fe.push_back (fe_1);
   fe.push_back (fe_2);
diff --git a/tests/hp/step-3c.cc b/tests/hp/step-3c.cc
index b4f885cc9c..ccb56f9cca 100644
--- a/tests/hp/step-3c.cc
+++ b/tests/hp/step-3c.cc
@@ -252,10 +252,10 @@ void LaplaceProblem::run ()
 {
   FE_Q<2> fe_1 (1),
        fe_2 (2),
-       fe_3 (3),
-       fe_4 (4),
-       fe_5 (5),
-       fe_6 (6);
+       fe_3 (QIterated<1>(QTrapez<1>(),3)),
+       fe_4 (QIterated<1>(QTrapez<1>(),4)),
+       fe_5 (QIterated<1>(QTrapez<1>(),5)),
+       fe_6 (QIterated<1>(QTrapez<1>(),6));
 
   fe.push_back (fe_1);
   fe.push_back (fe_2);
diff --git a/tests/hp/vectors_boundary_rhs_hp_01.cc b/tests/hp/vectors_boundary_rhs_hp_01.cc
index 7e16d7311a..fc111c1b98 100644
--- a/tests/hp/vectors_boundary_rhs_hp_01.cc
+++ b/tests/hp/vectors_boundary_rhs_hp_01.cc
@@ -86,8 +86,8 @@ check ()
   // of one Q1 and one Q2 element
   hp::FECollection<dim> element;
   for (unsigned int i=1; i<7-dim; ++i)
-    element.push_back (FESystem<dim> (FE_Q<dim>(i), 1,
-                                      FE_Q<dim>(i+1), 1));
+    element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
+                                      FE_Q<dim>(QIterated<1>(QTrapez<1>(),i+1)), 1));
   hp::DoFHandler<dim> dof(tr);
   for (typename hp::DoFHandler<dim>::active_cell_iterator
        cell = dof.begin_active(); cell!=dof.end(); ++cell)
diff --git a/tests/hp/vectors_boundary_rhs_hp_03.cc b/tests/hp/vectors_boundary_rhs_hp_03.cc
index 45a3c65420..32b8609b01 100644
--- a/tests/hp/vectors_boundary_rhs_hp_03.cc
+++ b/tests/hp/vectors_boundary_rhs_hp_03.cc
@@ -85,7 +85,7 @@ check ()
   // of one Q1 and one Q2 element
   hp::FECollection<dim> element;
   for (unsigned int i=1; i<7-dim; ++i)
-    element.push_back (FE_Q<dim>(i));
+    element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)));
   hp::DoFHandler<dim> dof(tr);
   for (typename hp::DoFHandler<dim>::active_cell_iterator
        cell = dof.begin_active(); cell!=dof.end(); ++cell)
diff --git a/tests/hp/vectors_rhs_hp_01.cc b/tests/hp/vectors_rhs_hp_01.cc
index 1c5f00c367..a409c0a817 100644
--- a/tests/hp/vectors_rhs_hp_01.cc
+++ b/tests/hp/vectors_rhs_hp_01.cc
@@ -86,8 +86,8 @@ check ()
   // of one Q1 and one Q2 element
   hp::FECollection<dim> element;
   for (unsigned int i=1; i<7-dim; ++i)
-    element.push_back (FESystem<dim> (FE_Q<dim>(i), 1,
-                                      FE_Q<dim>(i+1), 1));
+    element.push_back (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)), 1,
+                                      FE_Q<dim>(QIterated<1>(QTrapez<1>(),i+1)), 1));
   hp::DoFHandler<dim> dof(tr);
   for (typename hp::DoFHandler<dim>::active_cell_iterator
        cell = dof.begin_active(); cell!=dof.end(); ++cell)
diff --git a/tests/hp/vectors_rhs_hp_03.cc b/tests/hp/vectors_rhs_hp_03.cc
index d9bf4c8f88..a9f54765ef 100644
--- a/tests/hp/vectors_rhs_hp_03.cc
+++ b/tests/hp/vectors_rhs_hp_03.cc
@@ -85,7 +85,7 @@ check ()
   // of one Q1 and one Q2 element
   hp::FECollection<dim> element;
   for (unsigned int i=1; i<7-dim; ++i)
-    element.push_back (FE_Q<dim>(i));
+    element.push_back (FE_Q<dim>(QIterated<1>(QTrapez<1>(),i)));
   hp::DoFHandler<dim> dof(tr);
   for (typename hp::DoFHandler<dim>::active_cell_iterator
        cell = dof.begin_active(); cell!=dof.end(); ++cell)
diff --git a/tests/lac/constraint_graph.cc b/tests/lac/constraint_graph.cc
index a4b772c1ac..a7465d2ddc 100644
--- a/tests/lac/constraint_graph.cc
+++ b/tests/lac/constraint_graph.cc
@@ -30,6 +30,7 @@
 #include <deal.II/dofs/dof_tools.h>
 #include <deal.II/lac/constraint_matrix.h>
 #include <deal.II/fe/fe_q.h>
+#include <deal.II/base/quadrature_lib.h>
 
 #include <fstream>
 
@@ -47,8 +48,8 @@ void test ()
   hp::FECollection<dim> fe_collection;
   fe_collection.push_back(FE_Q<dim> (1));
   fe_collection.push_back(FE_Q<dim> (2));
-  fe_collection.push_back(FE_Q<dim> (3));
-  fe_collection.push_back(FE_Q<dim> (4));
+  fe_collection.push_back(FE_Q<dim> (QIterated<1>(QTrapez<1>(),3)));
+  fe_collection.push_back(FE_Q<dim> (QIterated<1>(QTrapez<1>(),4)));
 
   hp::DoFHandler<dim> dof_handler(tria);
 
diff --git a/tests/numerics/derivative_approximation.cc b/tests/numerics/derivative_approximation.cc
index 8a0b229619..a3f4fe285f 100644
--- a/tests/numerics/derivative_approximation.cc
+++ b/tests/numerics/derivative_approximation.cc
@@ -53,7 +53,7 @@ check ()
   if (dim==1)
     tr.refine_global(2);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tr);
   dof.distribute_dofs(element);
 
diff --git a/tests/numerics/error_estimator.cc b/tests/numerics/error_estimator.cc
index 4c65019442..6e3faed0e7 100644
--- a/tests/numerics/error_estimator.cc
+++ b/tests/numerics/error_estimator.cc
@@ -95,7 +95,7 @@ check ()
   if (dim==1)
     tr.refine_global(2);
 
-  FE_Q<dim> element(3);
+  FE_Q<dim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim> dof(tr);
   dof.distribute_dofs(element);
 
diff --git a/tests/numerics/error_estimator_01.cc b/tests/numerics/error_estimator_01.cc
index 761e4214ac..2bd9e14032 100644
--- a/tests/numerics/error_estimator_01.cc
+++ b/tests/numerics/error_estimator_01.cc
@@ -51,7 +51,7 @@ check ()
   tr.execute_coarsening_and_refinement ();
 
 
-  FE_Q<dim,spacedim> element(3);
+  FE_Q<dim,spacedim> element(QIterated<1>(QTrapez<1>(),3));
   DoFHandler<dim,spacedim> dof(tr);
   dof.distribute_dofs(element);
 
diff --git a/tests/numerics/error_estimator_02.cc b/tests/numerics/error_estimator_02.cc
index 31c2c99a80..2991f20b68 100644
--- a/tests/numerics/error_estimator_02.cc
+++ b/tests/numerics/error_estimator_02.cc
@@ -260,7 +260,7 @@ void test_neumann(const NeumanBC<dim> &func)
 
   const unsigned int p = 3;
 
-  fe_collection.push_back(dealii::FE_Q<dim>(p));
+  fe_collection.push_back(dealii::FE_Q<dim>(QIterated<1>(QTrapez<1>(),p)));
   quadrature_formula.push_back(dealii::QGauss<dim>(p+5));
   face_quadrature_formula.push_back(dealii::QGauss<dim-1>(p+5));
 
@@ -348,7 +348,7 @@ void test_regular(const MyFunction<dim> &func)
   for (unsigned int i=0; i<p_degree.size(); i++)
     {
       const unsigned int &p = p_degree[i];
-      fe_collection.push_back(dealii::FE_Q<dim>(p));
+      fe_collection.push_back(dealii::FE_Q<dim>(QIterated<1>(QTrapez<1>(),p)));
       quadrature_formula.push_back(dealii::QGauss<dim>(p+5));
       face_quadrature_formula.push_back(dealii::QGauss<dim-1>(p+5));
     }
@@ -462,7 +462,7 @@ void test_irregular(const MyFunction<dim> &func)
   for (unsigned int i=0; i<p_degree.size(); i++)
     {
       const unsigned int &p = p_degree[i];
-      fe_collection.push_back(dealii::FE_Q<dim>(p));
+      fe_collection.push_back(dealii::FE_Q<dim>(QIterated<1>(QTrapez<1>(),p)));
       quadrature_formula.push_back(dealii::QGauss<dim>(p+5));
       face_quadrature_formula.push_back(dealii::QGauss<dim-1>(p+5));
     }
@@ -631,7 +631,7 @@ void test(const MySecondFunction<dim> &func)
   dealii::ConstraintMatrix constraints;
   for (unsigned int p = 1; p <=3; p++)
     {
-      fe_collection.push_back(dealii::FE_Q<dim>(p));
+      fe_collection.push_back(dealii::FE_Q<dim>(QIterated<1>(QTrapez<1>(),p)));
       quadrature_formula.push_back(dealii::QGauss<dim>(p+1));
       face_quadrature_formula.push_back(dealii::QGauss<dim-1>(p+1));
     }
diff --git a/tests/numerics/no_flux_03.cc b/tests/numerics/no_flux_03.cc
index 92d95195df..6053806ce1 100644
--- a/tests/numerics/no_flux_03.cc
+++ b/tests/numerics/no_flux_03.cc
@@ -72,7 +72,7 @@ void test_hyper_sphere()
 
   for (unsigned int degree=1; degree<4; ++degree)
     {
-      FESystem<dim> fe (FE_Q<dim>(degree), dim);
+      FESystem<dim> fe (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim);
       test(tr, fe);
     }
 }
diff --git a/tests/numerics/no_flux_04.cc b/tests/numerics/no_flux_04.cc
index 2c360dc693..0525d9b4a0 100644
--- a/tests/numerics/no_flux_04.cc
+++ b/tests/numerics/no_flux_04.cc
@@ -131,7 +131,7 @@ void test_hyper_sphere()
 
   for (unsigned int degree=1; degree<6-dim; ++degree)
     {
-      FESystem<dim> fe (FE_Q<dim>(degree), dim);
+      FESystem<dim> fe (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim);
       test(tr, fe);
     }
 }
diff --git a/tests/numerics/no_flux_05.cc b/tests/numerics/no_flux_05.cc
index 8806a91ecc..52610dd2ba 100644
--- a/tests/numerics/no_flux_05.cc
+++ b/tests/numerics/no_flux_05.cc
@@ -85,7 +85,7 @@ void test_hyper_cube()
 
   for (unsigned int degree=1; degree<4; ++degree)
     {
-      FESystem<dim> fe (FE_Q<dim>(degree), dim,
+      FESystem<dim> fe (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim,
                         FE_DGP<dim>(degree+1), 1);
       test(tr, fe);
     }
diff --git a/tests/numerics/no_flux_hp_03.cc b/tests/numerics/no_flux_hp_03.cc
index a1c6e5d50f..18909705c7 100644
--- a/tests/numerics/no_flux_hp_03.cc
+++ b/tests/numerics/no_flux_hp_03.cc
@@ -66,7 +66,7 @@ void test_hyper_sphere()
 
   for (unsigned int degree=1; degree<4; ++degree)
     {
-      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(degree), dim));
+      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim));
       test(tr, fe);
     }
 }
diff --git a/tests/numerics/no_flux_hp_04.cc b/tests/numerics/no_flux_hp_04.cc
index adf29c3364..53830ec3c1 100644
--- a/tests/numerics/no_flux_hp_04.cc
+++ b/tests/numerics/no_flux_hp_04.cc
@@ -124,7 +124,7 @@ void test_hyper_sphere()
 
   for (unsigned int degree=1; degree<6-dim; ++degree)
     {
-      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(degree), dim));
+      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim));
       test(tr, fe);
     }
 }
diff --git a/tests/numerics/no_flux_hp_05.cc b/tests/numerics/no_flux_hp_05.cc
index e9bf4bdb39..786f20c51d 100644
--- a/tests/numerics/no_flux_hp_05.cc
+++ b/tests/numerics/no_flux_hp_05.cc
@@ -76,7 +76,7 @@ void test_hyper_cube()
 
   for (unsigned int degree=1; degree<4; ++degree)
     {
-      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(degree), dim,
+      hp::FECollection<dim> fe (FESystem<dim> (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim,
                                                FE_DGP<dim>(degree+1), 1));
       test(tr, fe);
     }
diff --git a/tests/numerics/normal_flux_03.cc b/tests/numerics/normal_flux_03.cc
index 404752835a..e5b155ef1b 100644
--- a/tests/numerics/normal_flux_03.cc
+++ b/tests/numerics/normal_flux_03.cc
@@ -67,7 +67,7 @@ void test_hyper_sphere()
 
   for (unsigned int degree=1; degree<4; ++degree)
     {
-      FESystem<dim> fe (FE_Q<dim>(degree), dim);
+      FESystem<dim> fe (FE_Q<dim>(QIterated<1>(QTrapez<1>(),degree)), dim);
       test(tr, fe);
     }
 }