From 0c17bd5fde6298c4165e8facb86c6855bfe3a62b Mon Sep 17 00:00:00 2001
From: Timo Heister <timo.heister@gmail.com>
Date: Mon, 31 Aug 2015 13:54:38 -0400
Subject: [PATCH] add test for H1div_seminorm

---
 tests/vector_tools/CMakeLists.txt             |   4 +
 tests/vector_tools/integrate_difference_01.cc | 109 ++++++++++++++++++
 .../integrate_difference_01.output            |   6 +
 3 files changed, 119 insertions(+)
 create mode 100644 tests/vector_tools/CMakeLists.txt
 create mode 100644 tests/vector_tools/integrate_difference_01.cc
 create mode 100644 tests/vector_tools/integrate_difference_01.output

diff --git a/tests/vector_tools/CMakeLists.txt b/tests/vector_tools/CMakeLists.txt
new file mode 100644
index 0000000000..f8ac3eb029
--- /dev/null
+++ b/tests/vector_tools/CMakeLists.txt
@@ -0,0 +1,4 @@
+CMAKE_MINIMUM_REQUIRED(VERSION 2.8.9)
+INCLUDE(../setup_testsubproject.cmake)
+PROJECT(testsuite CXX)
+DEAL_II_PICKUP_TESTS()
diff --git a/tests/vector_tools/integrate_difference_01.cc b/tests/vector_tools/integrate_difference_01.cc
new file mode 100644
index 0000000000..a94367eb3f
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01.cc
@@ -0,0 +1,109 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2014 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test integrate_difference
+
+#include "../tests.h"
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+
+using namespace dealii;
+
+
+// x+y(+z), x^2+y^2 (, z+xy)
+// div = 1+2y (+1)
+template <int dim>
+class Ref : public Function<dim>
+{
+  public:
+    Ref()
+		    :Function<dim>(dim)
+      {}
+    
+    double value (const Point<dim> &p, const unsigned int c) const
+      {
+	if (c==0)
+	  return p[0]+p[1]+((dim==3)?p[2]:0.0);
+	if (c==1)
+	  return p[0]*p[0]+p[1]*p[1];
+	if (c==2)
+	  return p[2]+p[0]*p[1];
+      }    
+};
+
+
+
+template <int dim>
+void test(VectorTools::NormType norm, double value)
+{
+  Triangulation<dim> tria;
+  GridGenerator::hyper_cube(tria);
+  tria.refine_global(1);
+
+  FESystem<dim> fe(FE_Q<dim>(4),dim);
+  DoFHandler<dim> dofh(tria);
+  dofh.distribute_dofs(fe);
+
+  Vector<double> solution (dofh.n_dofs ());
+  VectorTools::interpolate(dofh, Ref<dim>(), solution);
+  
+  Vector<double> cellwise_errors (tria.n_active_cells());
+  VectorTools::integrate_difference (dofh,
+				     solution,
+				     ZeroFunction<dim>(dim),
+				     cellwise_errors,
+				     QGauss<dim>(5),
+				     norm);
+  
+  const double error = cellwise_errors.l2_norm();
+
+  const double difference = std::abs(error-value);
+  deallog << "computed: " << error
+	  << " expected: " << value
+	  << " difference: " << difference
+	  << std::endl;
+  Assert(difference<1e-10, ExcMessage("Error in integrate_difference"));
+}
+
+template <int dim>
+void test()
+{
+  deallog << "Hdiv_seminorm:" << std::endl;
+  // sqrt(\int (div f)^2 = sqrt(\int (1+2y)^2)
+  test<dim>(VectorTools::Hdiv_seminorm, std::sqrt(13.0/3.0));
+  deallog << "L2_norm:" << std::endl;
+  // sqrt(\int_\Omega f^2) = sqrt(\int (x+y)^2+(x^2+y^2)^2)
+  test<dim>(VectorTools::L2_norm, std::sqrt(161.0/90.0));
+  
+  deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+  initlog();
+  test<2>();
+
+}
diff --git a/tests/vector_tools/integrate_difference_01.output b/tests/vector_tools/integrate_difference_01.output
new file mode 100644
index 0000000000..001f3d030a
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01.output
@@ -0,0 +1,6 @@
+
+DEAL::Hdiv_seminorm:
+DEAL::computed: 2.08167 expected: 2.08167 difference: 4.44089e-16
+DEAL::L2_norm:
+DEAL::computed: 1.33749 expected: 1.33749 difference: 2.22045e-16
+DEAL::OK
-- 
2.39.5