From: Luca Heltai <luca.heltai@sissa.it>
Date: Thu, 21 Dec 2017 16:32:01 +0000 (+0100)
Subject: Test singular integration on vertices.
X-Git-Tag: v9.0.0-rc1~583^2~7
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f45973fc2990458435122869e2ff3ebf7ef21cd9;p=dealii.git

Test singular integration on vertices.
---

diff --git a/tests/base/quadrature_simplex_06.cc b/tests/base/quadrature_simplex_06.cc
new file mode 100644
index 0000000000..67338b412c
--- /dev/null
+++ b/tests/base/quadrature_simplex_06.cc
@@ -0,0 +1,89 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 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.
+//
+// ---------------------------------------------------------------------
+
+// integrates the function *f(x,y)/R, where f(x,y) is a power of x and
+// y on the set [0,1]x[0,1]. dim = 2 only.
+
+#include "../tests.h"
+#include <deal.II/base/utilities.h>
+
+// all include files needed for the program
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/geometry_info.h>
+#include "simplex.h"
+
+
+int main()
+{
+  initlog();
+
+  deallog << std::endl
+          << "Calculation of the integral of f(x,y)*1/R on [0,1]x[0,1]" << std::endl
+          << "for f(x,y) = x^i y^j, with i,j ranging from 0 to 5, and R being" << std::endl
+          << "the distance from (x,y) to four vertices of the square." << std::endl
+          << std::endl;
+
+  double eps = 1e-10;
+
+  //       index  m  i  j
+  double error[4][6][6][6] = {{{{0}}}};
+
+  for (unsigned int m=0; m<6; ++m)
+    {
+      for (unsigned int index=0; index<4; ++index)
+        {
+          auto split_point = GeometryInfo<2>::unit_cell_vertex(index);
+
+          QSplit<2> quad(QTrianglePolar(m+1), split_point);
+
+          for (unsigned int i=0; i<6; ++i)
+            for (unsigned int j=0; j<6; ++j)
+              {
+                double exact_integral  = exact_integral_one_over_r(index, i,j);
+                double approx_integral = 0;
+
+                for (unsigned int q=0; q< quad.size(); ++q)
+                  {
+                    double x = quad.point(q)[0];
+                    double y = quad.point(q)[1];
+                    approx_integral += ( pow(x, (double)i) *
+                                         pow(y, (double)j) *
+                                         quad.weight(q) /
+                                         (quad.point(q)-split_point).norm());
+                  }
+                error[index][m][i][j] = approx_integral - exact_integral;
+              }
+        }
+    }
+
+
+  // Now output the results.
+  for (unsigned int index=0; index<4; ++index)
+    {
+      deallog << " ===============Vertex Index: "  << index
+              << " ==============================" << std::endl;
+      for (unsigned int i=0; i<6; ++i)
+        for (unsigned int j=0; j<6; ++j)
+          {
+            deallog << "======= f(x,y) = x^" << i
+                    << " y^" << j << std::endl;
+
+            for (unsigned int m=0; m<6; ++m)
+              deallog << "Order[" << m + 1 << "], error = "
+                      << error[index][m][i][j]  << std::endl;
+          }
+    }
+}
+
diff --git a/tests/base/quadrature_simplex_06.output b/tests/base/quadrature_simplex_06.output
new file mode 100644
index 0000000000..526a017ec1
--- /dev/null
+++ b/tests/base/quadrature_simplex_06.output
@@ -0,0 +1,1018 @@
+
+DEAL::
+DEAL::Calculation of the integral of f(x,y)*1/R on [0,1]x[0,1]
+DEAL::for f(x,y) = x^i y^j, with i,j ranging from 0 to 5, and R being
+DEAL::the distance from (x,y) to four vertices of the square.
+DEAL::
+DEAL:: ===============Vertex Index: 0 ==============================
+DEAL::======= f(x,y) = x^0 y^0
+DEAL::Order[1], error = -0.357784
+DEAL::Order[2], error = -0.0413770
+DEAL::Order[3], error = -0.00349564
+DEAL::Order[4], error = -0.000233484
+DEAL::Order[5], error = -1.19260e-05
+DEAL::Order[6], error = -3.91498e-07
+DEAL::======= f(x,y) = x^0 y^1
+DEAL::Order[1], error = -0.120932
+DEAL::Order[2], error = -0.0121220
+DEAL::Order[3], error = -0.000828723
+DEAL::Order[4], error = -3.88017e-05
+DEAL::Order[5], error = -7.85203e-07
+DEAL::Order[6], error = 4.39204e-08
+DEAL::======= f(x,y) = x^0 y^2
+DEAL::Order[1], error = -0.163072
+DEAL::Order[2], error = -0.0135078
+DEAL::Order[3], error = -0.00165252
+DEAL::Order[4], error = -0.000183000
+DEAL::Order[5], error = -1.90192e-05
+DEAL::Order[6], error = -1.88270e-06
+DEAL::======= f(x,y) = x^0 y^3
+DEAL::Order[1], error = -0.170372
+DEAL::Order[2], error = -0.0119124
+DEAL::Order[3], error = -0.00151573
+DEAL::Order[4], error = -0.000165201
+DEAL::Order[5], error = -1.62581e-05
+DEAL::Order[6], error = -1.49708e-06
+DEAL::======= f(x,y) = x^0 y^4
+DEAL::Order[1], error = -0.160373
+DEAL::Order[2], error = -0.0160819
+DEAL::Order[3], error = -0.00157738
+DEAL::Order[4], error = -0.000211312
+DEAL::Order[5], error = -2.67349e-05
+DEAL::Order[6], error = -3.25021e-06
+DEAL::======= f(x,y) = x^0 y^5
+DEAL::Order[1], error = -0.145363
+DEAL::Order[2], error = -0.0228780
+DEAL::Order[3], error = -0.00168236
+DEAL::Order[4], error = -0.000261625
+DEAL::Order[5], error = -3.71252e-05
+DEAL::Order[6], error = -4.86539e-06
+DEAL::======= f(x,y) = x^1 y^0
+DEAL::Order[1], error = -0.120932
+DEAL::Order[2], error = -0.0121220
+DEAL::Order[3], error = -0.000828723
+DEAL::Order[4], error = -3.88017e-05
+DEAL::Order[5], error = -7.85203e-07
+DEAL::Order[6], error = 4.39204e-08
+DEAL::======= f(x,y) = x^1 y^1
+DEAL::Order[1], error = -0.100522
+DEAL::Order[2], error = -0.00237035
+DEAL::Order[3], error = 6.02499e-05
+DEAL::Order[4], error = 2.60924e-05
+DEAL::Order[5], error = 2.92841e-06
+DEAL::Order[6], error = 1.89060e-07
+DEAL::======= f(x,y) = x^1 y^2
+DEAL::Order[1], error = -0.104301
+DEAL::Order[2], error = -0.00584758
+DEAL::Order[3], error = -0.000779842
+DEAL::Order[4], error = -9.82802e-05
+DEAL::Order[5], error = -1.16755e-05
+DEAL::Order[6], error = -1.29219e-06
+DEAL::======= f(x,y) = x^1 y^3
+DEAL::Order[1], error = -0.0944545
+DEAL::Order[2], error = -0.00931973
+DEAL::Order[3], error = -0.000844945
+DEAL::Order[4], error = -0.000100985
+DEAL::Order[5], error = -1.09354e-05
+DEAL::Order[6], error = -1.10179e-06
+DEAL::======= f(x,y) = x^1 y^4
+DEAL::Order[1], error = -0.0823104
+DEAL::Order[2], error = -0.0133881
+DEAL::Order[3], error = -0.00100812
+DEAL::Order[4], error = -0.000150114
+DEAL::Order[5], error = -2.05532e-05
+DEAL::Order[6], error = -2.62862e-06
+DEAL::======= f(x,y) = x^1 y^5
+DEAL::Order[1], error = -0.0714326
+DEAL::Order[2], error = -0.0170943
+DEAL::Order[3], error = -0.00136963
+DEAL::Order[4], error = -0.000201982
+DEAL::Order[5], error = -3.03423e-05
+DEAL::Order[6], error = -4.10185e-06
+DEAL::======= f(x,y) = x^2 y^0
+DEAL::Order[1], error = -0.163072
+DEAL::Order[2], error = -0.0135078
+DEAL::Order[3], error = -0.00165252
+DEAL::Order[4], error = -0.000183000
+DEAL::Order[5], error = -1.90192e-05
+DEAL::Order[6], error = -1.88270e-06
+DEAL::======= f(x,y) = x^2 y^1
+DEAL::Order[1], error = -0.104301
+DEAL::Order[2], error = -0.00584758
+DEAL::Order[3], error = -0.000779842
+DEAL::Order[4], error = -9.82802e-05
+DEAL::Order[5], error = -1.16755e-05
+DEAL::Order[6], error = -1.29219e-06
+DEAL::======= f(x,y) = x^2 y^2
+DEAL::Order[1], error = -0.0846154
+DEAL::Order[2], error = -0.0106738
+DEAL::Order[3], error = -0.00128390
+DEAL::Order[4], error = -0.000172904
+DEAL::Order[5], error = -2.04379e-05
+DEAL::Order[6], error = -2.18094e-06
+DEAL::======= f(x,y) = x^2 y^3
+DEAL::Order[1], error = -0.0687148
+DEAL::Order[2], error = -0.0135616
+DEAL::Order[3], error = -0.00125414
+DEAL::Order[4], error = -0.000162720
+DEAL::Order[5], error = -1.83607e-05
+DEAL::Order[6], error = -1.87415e-06
+DEAL::======= f(x,y) = x^2 y^4
+DEAL::Order[1], error = -0.0565925
+DEAL::Order[2], error = -0.0157408
+DEAL::Order[3], error = -0.00148226
+DEAL::Order[4], error = -0.000196011
+DEAL::Order[5], error = -2.55438e-05
+DEAL::Order[6], error = -3.07252e-06
+DEAL::======= f(x,y) = x^2 y^5
+DEAL::Order[1], error = -0.0475881
+DEAL::Order[2], error = -0.0172621
+DEAL::Order[3], error = -0.00192138
+DEAL::Order[4], error = -0.000235659
+DEAL::Order[5], error = -3.34854e-05
+DEAL::Order[6], error = -4.30612e-06
+DEAL::======= f(x,y) = x^3 y^0
+DEAL::Order[1], error = -0.170372
+DEAL::Order[2], error = -0.0119124
+DEAL::Order[3], error = -0.00151573
+DEAL::Order[4], error = -0.000165201
+DEAL::Order[5], error = -1.62581e-05
+DEAL::Order[6], error = -1.49708e-06
+DEAL::======= f(x,y) = x^3 y^1
+DEAL::Order[1], error = -0.0944545
+DEAL::Order[2], error = -0.00931973
+DEAL::Order[3], error = -0.000844945
+DEAL::Order[4], error = -0.000100985
+DEAL::Order[5], error = -1.09354e-05
+DEAL::Order[6], error = -1.10179e-06
+DEAL::======= f(x,y) = x^3 y^2
+DEAL::Order[1], error = -0.0687148
+DEAL::Order[2], error = -0.0135616
+DEAL::Order[3], error = -0.00125414
+DEAL::Order[4], error = -0.000162720
+DEAL::Order[5], error = -1.83607e-05
+DEAL::Order[6], error = -1.87415e-06
+DEAL::======= f(x,y) = x^3 y^3
+DEAL::Order[1], error = -0.0530451
+DEAL::Order[2], error = -0.0152722
+DEAL::Order[3], error = -0.00136928
+DEAL::Order[4], error = -0.000155446
+DEAL::Order[5], error = -1.68770e-05
+DEAL::Order[6], error = -1.65502e-06
+DEAL::======= f(x,y) = x^3 y^4
+DEAL::Order[1], error = -0.0425960
+DEAL::Order[2], error = -0.0161403
+DEAL::Order[3], error = -0.00172995
+DEAL::Order[4], error = -0.000185485
+DEAL::Order[5], error = -2.33477e-05
+DEAL::Order[6], error = -2.73098e-06
+DEAL::======= f(x,y) = x^3 y^5
+DEAL::Order[1], error = -0.0353374
+DEAL::Order[2], error = -0.0164924
+DEAL::Order[3], error = -0.00222715
+DEAL::Order[4], error = -0.000229151
+DEAL::Order[5], error = -3.06509e-05
+DEAL::Order[6], error = -3.86546e-06
+DEAL::======= f(x,y) = x^4 y^0
+DEAL::Order[1], error = -0.160373
+DEAL::Order[2], error = -0.0160819
+DEAL::Order[3], error = -0.00157738
+DEAL::Order[4], error = -0.000211312
+DEAL::Order[5], error = -2.67349e-05
+DEAL::Order[6], error = -3.25021e-06
+DEAL::======= f(x,y) = x^4 y^1
+DEAL::Order[1], error = -0.0823104
+DEAL::Order[2], error = -0.0133881
+DEAL::Order[3], error = -0.00100812
+DEAL::Order[4], error = -0.000150114
+DEAL::Order[5], error = -2.05532e-05
+DEAL::Order[6], error = -2.62862e-06
+DEAL::======= f(x,y) = x^4 y^2
+DEAL::Order[1], error = -0.0565925
+DEAL::Order[2], error = -0.0157408
+DEAL::Order[3], error = -0.00148226
+DEAL::Order[4], error = -0.000196011
+DEAL::Order[5], error = -2.55438e-05
+DEAL::Order[6], error = -3.07252e-06
+DEAL::======= f(x,y) = x^4 y^3
+DEAL::Order[1], error = -0.0425960
+DEAL::Order[2], error = -0.0161403
+DEAL::Order[3], error = -0.00172995
+DEAL::Order[4], error = -0.000185485
+DEAL::Order[5], error = -2.33477e-05
+DEAL::Order[6], error = -2.73098e-06
+DEAL::======= f(x,y) = x^4 y^4
+DEAL::Order[1], error = -0.0338211
+DEAL::Order[2], error = -0.0160073
+DEAL::Order[3], error = -0.00214733
+DEAL::Order[4], error = -0.000215779
+DEAL::Order[5], error = -2.83804e-05
+DEAL::Order[6], error = -3.56784e-06
+DEAL::======= f(x,y) = x^4 y^5
+DEAL::Order[1], error = -0.0279085
+DEAL::Order[2], error = -0.0156115
+DEAL::Order[3], error = -0.00262841
+DEAL::Order[4], error = -0.000267648
+DEAL::Order[5], error = -3.44500e-05
+DEAL::Order[6], error = -4.50519e-06
+DEAL::======= f(x,y) = x^5 y^0
+DEAL::Order[1], error = -0.145363
+DEAL::Order[2], error = -0.0228780
+DEAL::Order[3], error = -0.00168236
+DEAL::Order[4], error = -0.000261625
+DEAL::Order[5], error = -3.71252e-05
+DEAL::Order[6], error = -4.86539e-06
+DEAL::======= f(x,y) = x^5 y^1
+DEAL::Order[1], error = -0.0714326
+DEAL::Order[2], error = -0.0170943
+DEAL::Order[3], error = -0.00136963
+DEAL::Order[4], error = -0.000201982
+DEAL::Order[5], error = -3.03423e-05
+DEAL::Order[6], error = -4.10185e-06
+DEAL::======= f(x,y) = x^5 y^2
+DEAL::Order[1], error = -0.0475881
+DEAL::Order[2], error = -0.0172621
+DEAL::Order[3], error = -0.00192138
+DEAL::Order[4], error = -0.000235659
+DEAL::Order[5], error = -3.34854e-05
+DEAL::Order[6], error = -4.30612e-06
+DEAL::======= f(x,y) = x^5 y^3
+DEAL::Order[1], error = -0.0353374
+DEAL::Order[2], error = -0.0164924
+DEAL::Order[3], error = -0.00222715
+DEAL::Order[4], error = -0.000229151
+DEAL::Order[5], error = -3.06509e-05
+DEAL::Order[6], error = -3.86546e-06
+DEAL::======= f(x,y) = x^5 y^4
+DEAL::Order[1], error = -0.0279085
+DEAL::Order[2], error = -0.0156115
+DEAL::Order[3], error = -0.00262841
+DEAL::Order[4], error = -0.000267648
+DEAL::Order[5], error = -3.44500e-05
+DEAL::Order[6], error = -4.50519e-06
+DEAL::======= f(x,y) = x^5 y^5
+DEAL::Order[1], error = -0.0229813
+DEAL::Order[2], error = -0.0147180
+DEAL::Order[3], error = -0.00304408
+DEAL::Order[4], error = -0.000331203
+DEAL::Order[5], error = -3.97780e-05
+DEAL::Order[6], error = -5.27210e-06
+DEAL:: ===============Vertex Index: 1 ==============================
+DEAL::======= f(x,y) = x^0 y^0
+DEAL::Order[1], error = -0.357784
+DEAL::Order[2], error = -0.0413770
+DEAL::Order[3], error = -0.00349564
+DEAL::Order[4], error = -0.000233484
+DEAL::Order[5], error = -1.19260e-05
+DEAL::Order[6], error = -3.91498e-07
+DEAL::======= f(x,y) = x^0 y^1
+DEAL::Order[1], error = -0.120932
+DEAL::Order[2], error = -0.0121220
+DEAL::Order[3], error = -0.000828723
+DEAL::Order[4], error = -3.88017e-05
+DEAL::Order[5], error = -7.85203e-07
+DEAL::Order[6], error = 4.39204e-08
+DEAL::======= f(x,y) = x^0 y^2
+DEAL::Order[1], error = -0.163072
+DEAL::Order[2], error = -0.0135078
+DEAL::Order[3], error = -0.00165252
+DEAL::Order[4], error = -0.000183000
+DEAL::Order[5], error = -1.90192e-05
+DEAL::Order[6], error = -1.88270e-06
+DEAL::======= f(x,y) = x^0 y^3
+DEAL::Order[1], error = -0.170372
+DEAL::Order[2], error = -0.0119124
+DEAL::Order[3], error = -0.00151573
+DEAL::Order[4], error = -0.000165201
+DEAL::Order[5], error = -1.62581e-05
+DEAL::Order[6], error = -1.49708e-06
+DEAL::======= f(x,y) = x^0 y^4
+DEAL::Order[1], error = -0.160373
+DEAL::Order[2], error = -0.0160819
+DEAL::Order[3], error = -0.00157738
+DEAL::Order[4], error = -0.000211312
+DEAL::Order[5], error = -2.67349e-05
+DEAL::Order[6], error = -3.25021e-06
+DEAL::======= f(x,y) = x^0 y^5
+DEAL::Order[1], error = -0.145363
+DEAL::Order[2], error = -0.0228780
+DEAL::Order[3], error = -0.00168236
+DEAL::Order[4], error = -0.000261625
+DEAL::Order[5], error = -3.71252e-05
+DEAL::Order[6], error = -4.86539e-06
+DEAL::======= f(x,y) = x^1 y^0
+DEAL::Order[1], error = -0.236852
+DEAL::Order[2], error = -0.0292550
+DEAL::Order[3], error = -0.00266692
+DEAL::Order[4], error = -0.000194682
+DEAL::Order[5], error = -1.11408e-05
+DEAL::Order[6], error = -4.35418e-07
+DEAL::======= f(x,y) = x^1 y^1
+DEAL::Order[1], error = -0.0204105
+DEAL::Order[2], error = -0.00975165
+DEAL::Order[3], error = -0.000888973
+DEAL::Order[4], error = -6.48941e-05
+DEAL::Order[5], error = -3.71361e-06
+DEAL::Order[6], error = -1.45139e-07
+DEAL::======= f(x,y) = x^1 y^2
+DEAL::Order[1], error = -0.0587716
+DEAL::Order[2], error = -0.00766018
+DEAL::Order[3], error = -0.000872679
+DEAL::Order[4], error = -8.47202e-05
+DEAL::Order[5], error = -7.34372e-06
+DEAL::Order[6], error = -5.90510e-07
+DEAL::======= f(x,y) = x^1 y^3
+DEAL::Order[1], error = -0.0759180
+DEAL::Order[2], error = -0.00259262
+DEAL::Order[3], error = -0.000670785
+DEAL::Order[4], error = -6.42163e-05
+DEAL::Order[5], error = -5.32276e-06
+DEAL::Order[6], error = -3.95283e-07
+DEAL::======= f(x,y) = x^1 y^4
+DEAL::Order[1], error = -0.0780629
+DEAL::Order[2], error = -0.00269378
+DEAL::Order[3], error = -0.000569262
+DEAL::Order[4], error = -6.11988e-05
+DEAL::Order[5], error = -6.18176e-06
+DEAL::Order[6], error = -6.21591e-07
+DEAL::======= f(x,y) = x^1 y^5
+DEAL::Order[1], error = -0.0739299
+DEAL::Order[2], error = -0.00578370
+DEAL::Order[3], error = -0.000312725
+DEAL::Order[4], error = -5.96437e-05
+DEAL::Order[5], error = -6.78298e-06
+DEAL::Order[6], error = -7.63532e-07
+DEAL::======= f(x,y) = x^2 y^0
+DEAL::Order[1], error = -0.278992
+DEAL::Order[2], error = -0.0306407
+DEAL::Order[3], error = -0.00349072
+DEAL::Order[4], error = -0.000338881
+DEAL::Order[5], error = -2.93749e-05
+DEAL::Order[6], error = -2.36204e-06
+DEAL::======= f(x,y) = x^2 y^1
+DEAL::Order[1], error = -0.0241892
+DEAL::Order[2], error = -0.0132289
+DEAL::Order[3], error = -0.00172906
+DEAL::Order[4], error = -0.000189267
+DEAL::Order[5], error = -1.83175e-05
+DEAL::Order[6], error = -1.62639e-06
+DEAL::======= f(x,y) = x^2 y^2
+DEAL::Order[1], error = -0.0390863
+DEAL::Order[2], error = -0.0124864
+DEAL::Order[3], error = -0.00137673
+DEAL::Order[4], error = -0.000159344
+DEAL::Order[5], error = -1.61061e-05
+DEAL::Order[6], error = -1.47926e-06
+DEAL::======= f(x,y) = x^2 y^3
+DEAL::Order[1], error = -0.0501784
+DEAL::Order[2], error = -0.00683449
+DEAL::Order[3], error = -0.00107998
+DEAL::Order[4], error = -0.000125952
+DEAL::Order[5], error = -1.27481e-05
+DEAL::Order[6], error = -1.16764e-06
+DEAL::======= f(x,y) = x^2 y^4
+DEAL::Order[1], error = -0.0523451
+DEAL::Order[2], error = -0.00504646
+DEAL::Order[3], error = -0.00104341
+DEAL::Order[4], error = -0.000107097
+DEAL::Order[5], error = -1.11724e-05
+DEAL::Order[6], error = -1.06550e-06
+DEAL::======= f(x,y) = x^2 y^5
+DEAL::Order[1], error = -0.0500853
+DEAL::Order[2], error = -0.00595141
+DEAL::Order[3], error = -0.000864472
+DEAL::Order[4], error = -9.33207e-05
+DEAL::Order[5], error = -9.92611e-06
+DEAL::Order[6], error = -9.67794e-07
+DEAL::======= f(x,y) = x^3 y^0
+DEAL::Order[1], error = -0.313832
+DEAL::Order[2], error = -0.0336219
+DEAL::Order[3], error = -0.00445131
+DEAL::Order[4], error = -0.000500879
+DEAL::Order[5], error = -5.03700e-05
+DEAL::Order[6], error = -4.67429e-06
+DEAL::======= f(x,y) = x^3 y^1
+DEAL::Order[1], error = -0.0378142
+DEAL::Order[2], error = -0.0132340
+DEAL::Order[3], error = -0.00250405
+DEAL::Order[4], error = -0.000310935
+DEAL::Order[5], error = -3.36616e-05
+DEAL::Order[6], error = -3.29804e-06
+DEAL::======= f(x,y) = x^3 y^2
+DEAL::Order[1], error = -0.0353017
+DEAL::Order[2], error = -0.0144247
+DEAL::Order[3], error = -0.00191055
+DEAL::Order[4], error = -0.000244151
+DEAL::Order[5], error = -2.69456e-05
+DEAL::Order[6], error = -2.67480e-06
+DEAL::======= f(x,y) = x^3 y^3
+DEAL::Order[1], error = -0.0401084
+DEAL::Order[2], error = -0.00936574
+DEAL::Order[3], error = -0.00137404
+DEAL::Order[4], error = -0.000194961
+DEAL::Order[5], error = -2.16571e-05
+DEAL::Order[6], error = -2.15914e-06
+DEAL::======= f(x,y) = x^3 y^4
+DEAL::Order[1], error = -0.0406238
+DEAL::Order[2], error = -0.00699967
+DEAL::Order[3], error = -0.00126986
+DEAL::Order[4], error = -0.000163520
+DEAL::Order[5], error = -1.83590e-05
+DEAL::Order[6], error = -1.85094e-06
+DEAL::======= f(x,y) = x^3 y^5
+DEAL::Order[1], error = -0.0384915
+DEAL::Order[2], error = -0.00688875
+DEAL::Order[3], error = -0.00111045
+DEAL::Order[4], error = -0.000133506
+DEAL::Order[5], error = -1.59037e-05
+DEAL::Order[6], error = -1.61271e-06
+DEAL::======= f(x,y) = x^4 y^0
+DEAL::Order[1], error = -0.331372
+DEAL::Order[2], error = -0.0423680
+DEAL::Order[3], error = -0.00561033
+DEAL::Order[4], error = -0.000726788
+DEAL::Order[5], error = -8.46030e-05
+DEAL::Order[6], error = -9.12530e-06
+DEAL::======= f(x,y) = x^4 y^1
+DEAL::Order[1], error = -0.0491415
+DEAL::Order[2], error = -0.0138353
+DEAL::Order[3], error = -0.00337711
+DEAL::Order[4], error = -0.000479027
+DEAL::Order[5], error = -5.93636e-05
+DEAL::Order[6], error = -6.68691e-06
+DEAL::======= f(x,y) = x^4 y^2
+DEAL::Order[1], error = -0.0352954
+DEAL::Order[2], error = -0.0156544
+DEAL::Order[3], error = -0.00270223
+DEAL::Order[4], error = -0.000372433
+DEAL::Order[5], error = -4.70453e-05
+DEAL::Order[6], error = -5.37550e-06
+DEAL::======= f(x,y) = x^4 y^3
+DEAL::Order[1], error = -0.0352591
+DEAL::Order[2], error = -0.0110544
+DEAL::Order[3], error = -0.00191364
+DEAL::Order[4], error = -0.000301284
+DEAL::Order[5], error = -3.85204e-05
+DEAL::Order[6], error = -4.44573e-06
+DEAL::======= f(x,y) = x^4 y^4
+DEAL::Order[1], error = -0.0341240
+DEAL::Order[2], error = -0.00842045
+DEAL::Order[3], error = -0.00166600
+DEAL::Order[4], error = -0.000260764
+DEAL::Order[5], error = -3.27746e-05
+DEAL::Order[6], error = -3.81479e-06
+DEAL::======= f(x,y) = x^4 y^5
+DEAL::Order[1], error = -0.0317195
+DEAL::Order[2], error = -0.00771472
+DEAL::Order[3], error = -0.00145190
+DEAL::Order[4], error = -0.000218696
+DEAL::Order[5], error = -2.85150e-05
+DEAL::Order[6], error = -3.33802e-06
+DEAL::======= f(x,y) = x^5 y^0
+DEAL::Order[1], error = -0.336625
+DEAL::Order[2], error = -0.0542525
+DEAL::Order[3], error = -0.00692446
+DEAL::Order[4], error = -0.00101241
+DEAL::Order[5], error = -0.000132160
+DEAL::Order[6], error = -1.58530e-05
+DEAL::======= f(x,y) = x^5 y^1
+DEAL::Order[1], error = -0.0569045
+DEAL::Order[2], error = -0.0153951
+DEAL::Order[3], error = -0.00414988
+DEAL::Order[4], error = -0.000690805
+DEAL::Order[5], error = -9.52522e-05
+DEAL::Order[6], error = -1.18466e-05
+DEAL::======= f(x,y) = x^5 y^2
+DEAL::Order[1], error = -0.0359496
+DEAL::Order[2], error = -0.0168334
+DEAL::Order[3], error = -0.00354081
+DEAL::Order[4], error = -0.000537833
+DEAL::Order[5], error = -7.56468e-05
+DEAL::Order[6], error = -9.54614e-06
+DEAL::======= f(x,y) = x^5 y^3
+DEAL::Order[1], error = -0.0324400
+DEAL::Order[2], error = -0.0124164
+DEAL::Order[3], error = -0.00256226
+DEAL::Order[4], error = -0.000431293
+DEAL::Order[5], error = -6.25055e-05
+DEAL::Order[6], error = -7.96891e-06
+DEAL::======= f(x,y) = x^5 y^4
+DEAL::Order[1], error = -0.0299833
+DEAL::Order[2], error = -0.00957177
+DEAL::Order[3], error = -0.00216814
+DEAL::Order[4], error = -0.000377250
+DEAL::Order[5], error = -5.33820e-05
+DEAL::Order[6], error = -6.85655e-06
+DEAL::======= f(x,y) = x^5 y^5
+DEAL::Order[1], error = -0.0272677
+DEAL::Order[2], error = -0.00844182
+DEAL::Order[3], error = -0.00187441
+DEAL::Order[4], error = -0.000323834
+DEAL::Order[5], error = -4.62310e-05
+DEAL::Order[6], error = -6.01651e-06
+DEAL:: ===============Vertex Index: 2 ==============================
+DEAL::======= f(x,y) = x^0 y^0
+DEAL::Order[1], error = -0.357784
+DEAL::Order[2], error = -0.0413770
+DEAL::Order[3], error = -0.00349564
+DEAL::Order[4], error = -0.000233484
+DEAL::Order[5], error = -1.19260e-05
+DEAL::Order[6], error = -3.91498e-07
+DEAL::======= f(x,y) = x^0 y^1
+DEAL::Order[1], error = -0.236852
+DEAL::Order[2], error = -0.0292550
+DEAL::Order[3], error = -0.00266692
+DEAL::Order[4], error = -0.000194682
+DEAL::Order[5], error = -1.11408e-05
+DEAL::Order[6], error = -4.35418e-07
+DEAL::======= f(x,y) = x^0 y^2
+DEAL::Order[1], error = -0.278992
+DEAL::Order[2], error = -0.0306407
+DEAL::Order[3], error = -0.00349072
+DEAL::Order[4], error = -0.000338881
+DEAL::Order[5], error = -2.93749e-05
+DEAL::Order[6], error = -2.36204e-06
+DEAL::======= f(x,y) = x^0 y^3
+DEAL::Order[1], error = -0.313832
+DEAL::Order[2], error = -0.0336219
+DEAL::Order[3], error = -0.00445131
+DEAL::Order[4], error = -0.000500879
+DEAL::Order[5], error = -5.03700e-05
+DEAL::Order[6], error = -4.67429e-06
+DEAL::======= f(x,y) = x^0 y^4
+DEAL::Order[1], error = -0.331372
+DEAL::Order[2], error = -0.0423680
+DEAL::Order[3], error = -0.00561033
+DEAL::Order[4], error = -0.000726788
+DEAL::Order[5], error = -8.46030e-05
+DEAL::Order[6], error = -9.12530e-06
+DEAL::======= f(x,y) = x^0 y^5
+DEAL::Order[1], error = -0.336625
+DEAL::Order[2], error = -0.0542525
+DEAL::Order[3], error = -0.00692446
+DEAL::Order[4], error = -0.00101241
+DEAL::Order[5], error = -0.000132160
+DEAL::Order[6], error = -1.58530e-05
+DEAL::======= f(x,y) = x^1 y^0
+DEAL::Order[1], error = -0.120932
+DEAL::Order[2], error = -0.0121220
+DEAL::Order[3], error = -0.000828723
+DEAL::Order[4], error = -3.88017e-05
+DEAL::Order[5], error = -7.85203e-07
+DEAL::Order[6], error = 4.39204e-08
+DEAL::======= f(x,y) = x^1 y^1
+DEAL::Order[1], error = -0.0204105
+DEAL::Order[2], error = -0.00975165
+DEAL::Order[3], error = -0.000888973
+DEAL::Order[4], error = -6.48941e-05
+DEAL::Order[5], error = -3.71361e-06
+DEAL::Order[6], error = -1.45139e-07
+DEAL::======= f(x,y) = x^1 y^2
+DEAL::Order[1], error = -0.0241892
+DEAL::Order[2], error = -0.0132289
+DEAL::Order[3], error = -0.00172906
+DEAL::Order[4], error = -0.000189267
+DEAL::Order[5], error = -1.83175e-05
+DEAL::Order[6], error = -1.62639e-06
+DEAL::======= f(x,y) = x^1 y^3
+DEAL::Order[1], error = -0.0378142
+DEAL::Order[2], error = -0.0132340
+DEAL::Order[3], error = -0.00250405
+DEAL::Order[4], error = -0.000310935
+DEAL::Order[5], error = -3.36616e-05
+DEAL::Order[6], error = -3.29804e-06
+DEAL::======= f(x,y) = x^1 y^4
+DEAL::Order[1], error = -0.0491415
+DEAL::Order[2], error = -0.0138353
+DEAL::Order[3], error = -0.00337711
+DEAL::Order[4], error = -0.000479027
+DEAL::Order[5], error = -5.93636e-05
+DEAL::Order[6], error = -6.68691e-06
+DEAL::======= f(x,y) = x^1 y^5
+DEAL::Order[1], error = -0.0569045
+DEAL::Order[2], error = -0.0153951
+DEAL::Order[3], error = -0.00414988
+DEAL::Order[4], error = -0.000690805
+DEAL::Order[5], error = -9.52522e-05
+DEAL::Order[6], error = -1.18466e-05
+DEAL::======= f(x,y) = x^2 y^0
+DEAL::Order[1], error = -0.163072
+DEAL::Order[2], error = -0.0135078
+DEAL::Order[3], error = -0.00165252
+DEAL::Order[4], error = -0.000183000
+DEAL::Order[5], error = -1.90192e-05
+DEAL::Order[6], error = -1.88270e-06
+DEAL::======= f(x,y) = x^2 y^1
+DEAL::Order[1], error = -0.0587716
+DEAL::Order[2], error = -0.00766018
+DEAL::Order[3], error = -0.000872679
+DEAL::Order[4], error = -8.47202e-05
+DEAL::Order[5], error = -7.34372e-06
+DEAL::Order[6], error = -5.90510e-07
+DEAL::======= f(x,y) = x^2 y^2
+DEAL::Order[1], error = -0.0390863
+DEAL::Order[2], error = -0.0124864
+DEAL::Order[3], error = -0.00137673
+DEAL::Order[4], error = -0.000159344
+DEAL::Order[5], error = -1.61061e-05
+DEAL::Order[6], error = -1.47926e-06
+DEAL::======= f(x,y) = x^2 y^3
+DEAL::Order[1], error = -0.0353017
+DEAL::Order[2], error = -0.0144247
+DEAL::Order[3], error = -0.00191055
+DEAL::Order[4], error = -0.000244151
+DEAL::Order[5], error = -2.69456e-05
+DEAL::Order[6], error = -2.67480e-06
+DEAL::======= f(x,y) = x^2 y^4
+DEAL::Order[1], error = -0.0352954
+DEAL::Order[2], error = -0.0156544
+DEAL::Order[3], error = -0.00270223
+DEAL::Order[4], error = -0.000372433
+DEAL::Order[5], error = -4.70453e-05
+DEAL::Order[6], error = -5.37550e-06
+DEAL::======= f(x,y) = x^2 y^5
+DEAL::Order[1], error = -0.0359496
+DEAL::Order[2], error = -0.0168334
+DEAL::Order[3], error = -0.00354081
+DEAL::Order[4], error = -0.000537833
+DEAL::Order[5], error = -7.56468e-05
+DEAL::Order[6], error = -9.54614e-06
+DEAL::======= f(x,y) = x^3 y^0
+DEAL::Order[1], error = -0.170372
+DEAL::Order[2], error = -0.0119124
+DEAL::Order[3], error = -0.00151573
+DEAL::Order[4], error = -0.000165201
+DEAL::Order[5], error = -1.62581e-05
+DEAL::Order[6], error = -1.49708e-06
+DEAL::======= f(x,y) = x^3 y^1
+DEAL::Order[1], error = -0.0759180
+DEAL::Order[2], error = -0.00259262
+DEAL::Order[3], error = -0.000670785
+DEAL::Order[4], error = -6.42163e-05
+DEAL::Order[5], error = -5.32276e-06
+DEAL::Order[6], error = -3.95283e-07
+DEAL::======= f(x,y) = x^3 y^2
+DEAL::Order[1], error = -0.0501784
+DEAL::Order[2], error = -0.00683449
+DEAL::Order[3], error = -0.00107998
+DEAL::Order[4], error = -0.000125952
+DEAL::Order[5], error = -1.27481e-05
+DEAL::Order[6], error = -1.16764e-06
+DEAL::======= f(x,y) = x^3 y^3
+DEAL::Order[1], error = -0.0401084
+DEAL::Order[2], error = -0.00936574
+DEAL::Order[3], error = -0.00137404
+DEAL::Order[4], error = -0.000194961
+DEAL::Order[5], error = -2.16571e-05
+DEAL::Order[6], error = -2.15914e-06
+DEAL::======= f(x,y) = x^3 y^4
+DEAL::Order[1], error = -0.0352591
+DEAL::Order[2], error = -0.0110544
+DEAL::Order[3], error = -0.00191364
+DEAL::Order[4], error = -0.000301284
+DEAL::Order[5], error = -3.85204e-05
+DEAL::Order[6], error = -4.44573e-06
+DEAL::======= f(x,y) = x^3 y^5
+DEAL::Order[1], error = -0.0324400
+DEAL::Order[2], error = -0.0124164
+DEAL::Order[3], error = -0.00256226
+DEAL::Order[4], error = -0.000431293
+DEAL::Order[5], error = -6.25055e-05
+DEAL::Order[6], error = -7.96891e-06
+DEAL::======= f(x,y) = x^4 y^0
+DEAL::Order[1], error = -0.160373
+DEAL::Order[2], error = -0.0160819
+DEAL::Order[3], error = -0.00157738
+DEAL::Order[4], error = -0.000211312
+DEAL::Order[5], error = -2.67349e-05
+DEAL::Order[6], error = -3.25021e-06
+DEAL::======= f(x,y) = x^4 y^1
+DEAL::Order[1], error = -0.0780629
+DEAL::Order[2], error = -0.00269378
+DEAL::Order[3], error = -0.000569262
+DEAL::Order[4], error = -6.11988e-05
+DEAL::Order[5], error = -6.18176e-06
+DEAL::Order[6], error = -6.21591e-07
+DEAL::======= f(x,y) = x^4 y^2
+DEAL::Order[1], error = -0.0523451
+DEAL::Order[2], error = -0.00504646
+DEAL::Order[3], error = -0.00104341
+DEAL::Order[4], error = -0.000107097
+DEAL::Order[5], error = -1.11724e-05
+DEAL::Order[6], error = -1.06550e-06
+DEAL::======= f(x,y) = x^4 y^3
+DEAL::Order[1], error = -0.0406238
+DEAL::Order[2], error = -0.00699967
+DEAL::Order[3], error = -0.00126986
+DEAL::Order[4], error = -0.000163520
+DEAL::Order[5], error = -1.83590e-05
+DEAL::Order[6], error = -1.85094e-06
+DEAL::======= f(x,y) = x^4 y^4
+DEAL::Order[1], error = -0.0341240
+DEAL::Order[2], error = -0.00842045
+DEAL::Order[3], error = -0.00166600
+DEAL::Order[4], error = -0.000260764
+DEAL::Order[5], error = -3.27746e-05
+DEAL::Order[6], error = -3.81479e-06
+DEAL::======= f(x,y) = x^4 y^5
+DEAL::Order[1], error = -0.0299833
+DEAL::Order[2], error = -0.00957177
+DEAL::Order[3], error = -0.00216814
+DEAL::Order[4], error = -0.000377250
+DEAL::Order[5], error = -5.33820e-05
+DEAL::Order[6], error = -6.85655e-06
+DEAL::======= f(x,y) = x^5 y^0
+DEAL::Order[1], error = -0.145363
+DEAL::Order[2], error = -0.0228780
+DEAL::Order[3], error = -0.00168236
+DEAL::Order[4], error = -0.000261625
+DEAL::Order[5], error = -3.71252e-05
+DEAL::Order[6], error = -4.86539e-06
+DEAL::======= f(x,y) = x^5 y^1
+DEAL::Order[1], error = -0.0739299
+DEAL::Order[2], error = -0.00578370
+DEAL::Order[3], error = -0.000312725
+DEAL::Order[4], error = -5.96437e-05
+DEAL::Order[5], error = -6.78298e-06
+DEAL::Order[6], error = -7.63532e-07
+DEAL::======= f(x,y) = x^5 y^2
+DEAL::Order[1], error = -0.0500853
+DEAL::Order[2], error = -0.00595141
+DEAL::Order[3], error = -0.000864472
+DEAL::Order[4], error = -9.33207e-05
+DEAL::Order[5], error = -9.92611e-06
+DEAL::Order[6], error = -9.67794e-07
+DEAL::======= f(x,y) = x^5 y^3
+DEAL::Order[1], error = -0.0384915
+DEAL::Order[2], error = -0.00688875
+DEAL::Order[3], error = -0.00111045
+DEAL::Order[4], error = -0.000133506
+DEAL::Order[5], error = -1.59037e-05
+DEAL::Order[6], error = -1.61271e-06
+DEAL::======= f(x,y) = x^5 y^4
+DEAL::Order[1], error = -0.0317195
+DEAL::Order[2], error = -0.00771472
+DEAL::Order[3], error = -0.00145190
+DEAL::Order[4], error = -0.000218696
+DEAL::Order[5], error = -2.85150e-05
+DEAL::Order[6], error = -3.33802e-06
+DEAL::======= f(x,y) = x^5 y^5
+DEAL::Order[1], error = -0.0272677
+DEAL::Order[2], error = -0.00844182
+DEAL::Order[3], error = -0.00187441
+DEAL::Order[4], error = -0.000323834
+DEAL::Order[5], error = -4.62310e-05
+DEAL::Order[6], error = -6.01651e-06
+DEAL:: ===============Vertex Index: 3 ==============================
+DEAL::======= f(x,y) = x^0 y^0
+DEAL::Order[1], error = -0.357784
+DEAL::Order[2], error = -0.0413770
+DEAL::Order[3], error = -0.00349564
+DEAL::Order[4], error = -0.000233484
+DEAL::Order[5], error = -1.19260e-05
+DEAL::Order[6], error = -3.91498e-07
+DEAL::======= f(x,y) = x^0 y^1
+DEAL::Order[1], error = -0.236852
+DEAL::Order[2], error = -0.0292550
+DEAL::Order[3], error = -0.00266692
+DEAL::Order[4], error = -0.000194682
+DEAL::Order[5], error = -1.11408e-05
+DEAL::Order[6], error = -4.35418e-07
+DEAL::======= f(x,y) = x^0 y^2
+DEAL::Order[1], error = -0.278992
+DEAL::Order[2], error = -0.0306407
+DEAL::Order[3], error = -0.00349072
+DEAL::Order[4], error = -0.000338881
+DEAL::Order[5], error = -2.93749e-05
+DEAL::Order[6], error = -2.36204e-06
+DEAL::======= f(x,y) = x^0 y^3
+DEAL::Order[1], error = -0.313832
+DEAL::Order[2], error = -0.0336219
+DEAL::Order[3], error = -0.00445131
+DEAL::Order[4], error = -0.000500879
+DEAL::Order[5], error = -5.03700e-05
+DEAL::Order[6], error = -4.67429e-06
+DEAL::======= f(x,y) = x^0 y^4
+DEAL::Order[1], error = -0.331372
+DEAL::Order[2], error = -0.0423680
+DEAL::Order[3], error = -0.00561033
+DEAL::Order[4], error = -0.000726788
+DEAL::Order[5], error = -8.46030e-05
+DEAL::Order[6], error = -9.12530e-06
+DEAL::======= f(x,y) = x^0 y^5
+DEAL::Order[1], error = -0.336625
+DEAL::Order[2], error = -0.0542525
+DEAL::Order[3], error = -0.00692446
+DEAL::Order[4], error = -0.00101241
+DEAL::Order[5], error = -0.000132160
+DEAL::Order[6], error = -1.58530e-05
+DEAL::======= f(x,y) = x^1 y^0
+DEAL::Order[1], error = -0.236852
+DEAL::Order[2], error = -0.0292550
+DEAL::Order[3], error = -0.00266692
+DEAL::Order[4], error = -0.000194682
+DEAL::Order[5], error = -1.11408e-05
+DEAL::Order[6], error = -4.35418e-07
+DEAL::======= f(x,y) = x^1 y^1
+DEAL::Order[1], error = -0.216441
+DEAL::Order[2], error = -0.0195033
+DEAL::Order[3], error = -0.00177795
+DEAL::Order[4], error = -0.000129788
+DEAL::Order[5], error = -7.42723e-06
+DEAL::Order[6], error = -2.90279e-07
+DEAL::======= f(x,y) = x^1 y^2
+DEAL::Order[1], error = -0.254802
+DEAL::Order[2], error = -0.0174118
+DEAL::Order[3], error = -0.00176165
+DEAL::Order[4], error = -0.000149614
+DEAL::Order[5], error = -1.10573e-05
+DEAL::Order[6], error = -7.35650e-07
+DEAL::======= f(x,y) = x^1 y^3
+DEAL::Order[1], error = -0.276017
+DEAL::Order[2], error = -0.0203879
+DEAL::Order[3], error = -0.00194725
+DEAL::Order[4], error = -0.000189944
+DEAL::Order[5], error = -1.67084e-05
+DEAL::Order[6], error = -1.37625e-06
+DEAL::======= f(x,y) = x^1 y^4
+DEAL::Order[1], error = -0.282231
+DEAL::Order[2], error = -0.0285327
+DEAL::Order[3], error = -0.00223322
+DEAL::Order[4], error = -0.000247761
+DEAL::Order[5], error = -2.52394e-05
+DEAL::Order[6], error = -2.43838e-06
+DEAL::======= f(x,y) = x^1 y^5
+DEAL::Order[1], error = -0.279720
+DEAL::Order[2], error = -0.0388575
+DEAL::Order[3], error = -0.00277458
+DEAL::Order[4], error = -0.000321602
+DEAL::Order[5], error = -3.69082e-05
+DEAL::Order[6], error = -4.00642e-06
+DEAL::======= f(x,y) = x^2 y^0
+DEAL::Order[1], error = -0.278992
+DEAL::Order[2], error = -0.0306407
+DEAL::Order[3], error = -0.00349072
+DEAL::Order[4], error = -0.000338881
+DEAL::Order[5], error = -2.93749e-05
+DEAL::Order[6], error = -2.36204e-06
+DEAL::======= f(x,y) = x^2 y^1
+DEAL::Order[1], error = -0.254802
+DEAL::Order[2], error = -0.0174118
+DEAL::Order[3], error = -0.00176165
+DEAL::Order[4], error = -0.000149614
+DEAL::Order[5], error = -1.10573e-05
+DEAL::Order[6], error = -7.35650e-07
+DEAL::======= f(x,y) = x^2 y^2
+DEAL::Order[1], error = -0.269700
+DEAL::Order[2], error = -0.0166693
+DEAL::Order[3], error = -0.00140932
+DEAL::Order[4], error = -0.000119691
+DEAL::Order[5], error = -8.84587e-06
+DEAL::Order[6], error = -5.88520e-07
+DEAL::======= f(x,y) = x^2 y^3
+DEAL::Order[1], error = -0.273505
+DEAL::Order[2], error = -0.0215786
+DEAL::Order[3], error = -0.00135375
+DEAL::Order[4], error = -0.000123161
+DEAL::Order[5], error = -9.99240e-06
+DEAL::Order[6], error = -7.53009e-07
+DEAL::======= f(x,y) = x^2 y^4
+DEAL::Order[1], error = -0.268385
+DEAL::Order[2], error = -0.0303518
+DEAL::Order[3], error = -0.00155835
+DEAL::Order[4], error = -0.000141166
+DEAL::Order[5], error = -1.29212e-05
+DEAL::Order[6], error = -1.12697e-06
+DEAL::======= f(x,y) = x^2 y^5
+DEAL::Order[1], error = -0.258765
+DEAL::Order[2], error = -0.0402958
+DEAL::Order[3], error = -0.00216550
+DEAL::Order[4], error = -0.000168629
+DEAL::Order[5], error = -1.73028e-05
+DEAL::Order[6], error = -1.70596e-06
+DEAL::======= f(x,y) = x^3 y^0
+DEAL::Order[1], error = -0.313832
+DEAL::Order[2], error = -0.0336219
+DEAL::Order[3], error = -0.00445131
+DEAL::Order[4], error = -0.000500879
+DEAL::Order[5], error = -5.03700e-05
+DEAL::Order[6], error = -4.67429e-06
+DEAL::======= f(x,y) = x^3 y^1
+DEAL::Order[1], error = -0.276017
+DEAL::Order[2], error = -0.0203879
+DEAL::Order[3], error = -0.00194725
+DEAL::Order[4], error = -0.000189944
+DEAL::Order[5], error = -1.67084e-05
+DEAL::Order[6], error = -1.37625e-06
+DEAL::======= f(x,y) = x^3 y^2
+DEAL::Order[1], error = -0.273505
+DEAL::Order[2], error = -0.0215786
+DEAL::Order[3], error = -0.00135375
+DEAL::Order[4], error = -0.000123161
+DEAL::Order[5], error = -9.99240e-06
+DEAL::Order[6], error = -7.53009e-07
+DEAL::======= f(x,y) = x^3 y^3
+DEAL::Order[1], error = -0.266185
+DEAL::Order[2], error = -0.0278283
+DEAL::Order[3], error = -0.00129674
+DEAL::Order[4], error = -0.000105566
+DEAL::Order[5], error = -8.56491e-06
+DEAL::Order[6], error = -6.45437e-07
+DEAL::======= f(x,y) = x^3 y^4
+DEAL::Order[1], error = -0.254575
+DEAL::Order[2], error = -0.0367709
+DEAL::Order[3], error = -0.00167207
+DEAL::Order[4], error = -0.000105720
+DEAL::Order[5], error = -9.12791e-06
+DEAL::Order[6], error = -7.45333e-07
+DEAL::======= f(x,y) = x^3 y^5
+DEAL::Order[1], error = -0.241320
+DEAL::Order[2], error = -0.0461511
+DEAL::Order[3], error = -0.00253497
+DEAL::Order[4], error = -0.000122197
+DEAL::Order[5], error = -1.08387e-05
+DEAL::Order[6], error = -9.82727e-07
+DEAL::======= f(x,y) = x^4 y^0
+DEAL::Order[1], error = -0.331372
+DEAL::Order[2], error = -0.0423680
+DEAL::Order[3], error = -0.00561033
+DEAL::Order[4], error = -0.000726788
+DEAL::Order[5], error = -8.46030e-05
+DEAL::Order[6], error = -9.12530e-06
+DEAL::======= f(x,y) = x^4 y^1
+DEAL::Order[1], error = -0.282231
+DEAL::Order[2], error = -0.0285327
+DEAL::Order[3], error = -0.00223322
+DEAL::Order[4], error = -0.000247761
+DEAL::Order[5], error = -2.52394e-05
+DEAL::Order[6], error = -2.43838e-06
+DEAL::======= f(x,y) = x^4 y^2
+DEAL::Order[1], error = -0.268385
+DEAL::Order[2], error = -0.0303518
+DEAL::Order[3], error = -0.00155835
+DEAL::Order[4], error = -0.000141166
+DEAL::Order[5], error = -1.29212e-05
+DEAL::Order[6], error = -1.12697e-06
+DEAL::======= f(x,y) = x^4 y^3
+DEAL::Order[1], error = -0.254575
+DEAL::Order[2], error = -0.0367709
+DEAL::Order[3], error = -0.00167207
+DEAL::Order[4], error = -0.000105720
+DEAL::Order[5], error = -9.12791e-06
+DEAL::Order[6], error = -7.45333e-07
+DEAL::======= f(x,y) = x^4 y^4
+DEAL::Order[1], error = -0.239666
+DEAL::Order[2], error = -0.0451559
+DEAL::Order[3], error = -0.00232675
+DEAL::Order[4], error = -0.000100903
+DEAL::Order[5], error = -8.11370e-06
+DEAL::Order[6], error = -6.62518e-07
+DEAL::======= f(x,y) = x^4 y^5
+DEAL::Order[1], error = -0.224928
+DEAL::Order[2], error = -0.0535787
+DEAL::Order[3], error = -0.00348887
+DEAL::Order[4], error = -0.000128263
+DEAL::Order[5], error = -8.39231e-06
+DEAL::Order[6], error = -7.24350e-07
+DEAL::======= f(x,y) = x^5 y^0
+DEAL::Order[1], error = -0.336625
+DEAL::Order[2], error = -0.0542525
+DEAL::Order[3], error = -0.00692446
+DEAL::Order[4], error = -0.00101241
+DEAL::Order[5], error = -0.000132160
+DEAL::Order[6], error = -1.58530e-05
+DEAL::======= f(x,y) = x^5 y^1
+DEAL::Order[1], error = -0.279720
+DEAL::Order[2], error = -0.0388575
+DEAL::Order[3], error = -0.00277458
+DEAL::Order[4], error = -0.000321602
+DEAL::Order[5], error = -3.69082e-05
+DEAL::Order[6], error = -4.00642e-06
+DEAL::======= f(x,y) = x^5 y^2
+DEAL::Order[1], error = -0.258765
+DEAL::Order[2], error = -0.0402958
+DEAL::Order[3], error = -0.00216550
+DEAL::Order[4], error = -0.000168629
+DEAL::Order[5], error = -1.73028e-05
+DEAL::Order[6], error = -1.70596e-06
+DEAL::======= f(x,y) = x^5 y^3
+DEAL::Order[1], error = -0.241320
+DEAL::Order[2], error = -0.0461511
+DEAL::Order[3], error = -0.00253497
+DEAL::Order[4], error = -0.000122197
+DEAL::Order[5], error = -1.08387e-05
+DEAL::Order[6], error = -9.82727e-07
+DEAL::======= f(x,y) = x^5 y^4
+DEAL::Order[1], error = -0.224928
+DEAL::Order[2], error = -0.0535787
+DEAL::Order[3], error = -0.00348887
+DEAL::Order[4], error = -0.000128263
+DEAL::Order[5], error = -8.39231e-06
+DEAL::Order[6], error = -7.24350e-07
+DEAL::======= f(x,y) = x^5 y^5
+DEAL::Order[1], error = -0.209847
+DEAL::Order[2], error = -0.0608639
+DEAL::Order[3], error = -0.00492680
+DEAL::Order[4], error = -0.000186200
+DEAL::Order[5], error = -7.99132e-06
+DEAL::Order[6], error = -6.58500e-07
diff --git a/tests/base/simplex.h b/tests/base/simplex.h
index 5eefe544fa..a6e92c1d71 100644
--- a/tests/base/simplex.h
+++ b/tests/base/simplex.h
@@ -52,4 +52,188 @@ std::array<Point<3>, 4> get_simplex()
 }
 
 
+// Exact integral of 1/R times a polynomial computed using Maple.
+double exact_integral_one_over_r(const unsigned int vertex_index,
+                                 const unsigned int i,
+                                 const unsigned int j)
+{
+  Assert(vertex_index < 4, ExcInternalError());
+  Assert(i<6, ExcNotImplemented());
+  Assert(j<6, ExcNotImplemented());
+
+  // The integrals are computed using the following maple snippet of
+  // code:
+  //
+  //  sing_int := proc(index, N, M)
+  //     if index = 0 then
+  //        return int(int(x^N *y^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
+  //     elif index = 1 then
+  //        return int(int(x^N *y^M/sqrt((x-1)^2+y^2), x=0.0..1.0), y=0.0..1.0);
+  //     elif index = 2 then
+  //        return int(int(x^N *y^M/sqrt(x^2+(y-1)^2), x=0.0..1.0), y=0.0..1.0);
+  //     elif index = 3 then
+  //        return int(int((1-x)^N *(1-y)^M/sqrt(x^2+y^2), x=0.0..1.0), y=0.0..1.0);
+  //     end if;
+  //  end proc;
+  //  Digits := 20;
+  //  for i from 3 to 3 do
+  //     for n from 0 to 5 do
+  //      for m from 0 to 5 do
+  //           C( v[i+1][n+1][m+1] = sing_int(i, n, m), resultname="a");
+  //        end do;
+  //     end do;
+  //  end do;
+
+  static double v[4][6][6] = {{{0}}};
+  if (v[0][0][0] == 0)
+    {
+      v[0][0][0] = 0.17627471740390860505e1;
+      v[0][0][1] = 0.64779357469631903702e0;
+      v[0][0][2] = 0.38259785823210634567e0;
+      v[0][0][3] = 0.26915893322379450224e0;
+      v[0][0][4] = 0.20702239737104695572e0;
+      v[0][0][5] = 0.16800109713227567467e0;
+      v[0][1][0] = 0.64779357469631903702e0;
+      v[0][1][1] = 0.27614237491539669920e0;
+      v[0][1][2] = 0.17015838751246776515e0;
+      v[0][1][3] = 0.12189514164974600651e0;
+      v[0][1][4] = 0.94658660368131133694e-1;
+      v[0][1][5] = 0.77263794021029438797e-1;
+      v[0][2][0] = 0.38259785823210634567e0;
+      v[0][2][1] = 0.17015838751246776515e0;
+      v[0][2][2] = 0.10656799507071040471e0;
+      v[0][2][3] = 0.76947022258735165920e-1;
+      v[0][2][4] = 0.60022626787495395021e-1;
+      v[0][2][5] = 0.49131622931360879320e-1;
+      v[0][3][0] = 0.26915893322379450224e0;
+      v[0][3][1] = 0.12189514164974600651e0;
+      v[0][3][2] = 0.76947022258735165919e-1;
+      v[0][3][3] = 0.55789184535895709637e-1;
+      v[0][3][4] = 0.43625068213915842136e-1;
+      v[0][3][5] = 0.35766126849971778500e-1;
+      v[0][4][0] = 0.20702239737104695572e0;
+      v[0][4][1] = 0.94658660368131133694e-1;
+      v[0][4][2] = 0.60022626787495395021e-1;
+      v[0][4][3] = 0.43625068213915842137e-1;
+      v[0][4][4] = 0.34164088852375945192e-1;
+      v[0][4][5] = 0.28037139560980277614e-1;
+      v[0][5][0] = 0.16800109713227567467e0;
+      v[0][5][1] = 0.77263794021029438797e-1;
+      v[0][5][2] = 0.49131622931360879320e-1;
+      v[0][5][3] = 0.35766126849971778501e-1;
+      v[0][5][4] = 0.28037139560980277614e-1;
+      v[0][5][5] = 0.23024181049838367777e-1;
+      v[1][0][0] = 0.17627471740390860505e1;
+      v[1][0][1] = 0.64779357469631903702e0;
+      v[1][0][2] = 0.38259785823210634567e0;
+      v[1][0][3] = 0.26915893322379450224e0;
+      v[1][0][4] = 0.20702239737104695572e0;
+      v[1][0][5] = 0.16800109713227567467e0;
+      v[1][1][0] = 0.11149535993427670134e1;
+      v[1][1][1] = 0.37165119978092233782e0;
+      v[1][1][2] = 0.21243947071963858053e0;
+      v[1][1][3] = 0.14726379157404849573e0;
+      v[1][1][4] = 0.11236373700291582202e0;
+      v[1][1][5] = 0.90737303111246235871e-1;
+      v[1][2][0] = 0.84975788287855432210e0;
+      v[1][2][1] = 0.26566721237799340376e0;
+      v[1][2][2] = 0.14884907827788122009e0;
+      v[1][2][3] = 0.10231567218303765515e0;
+      v[1][2][4] = 0.77727703422280083352e-1;
+      v[1][2][5] = 0.62605132021577676395e-1;
+      v[1][3][0] = 0.69800109142265347423e0;
+      v[1][3][1] = 0.20794647083778622837e0;
+      v[1][3][2] = 0.11487965864809909847e0;
+      v[1][3][3] = 0.78525390514866270852e-1;
+      v[1][3][4] = 0.59489228415223897572e-1;
+      v[1][3][5] = 0.47838457013298217744e-1;
+      v[1][4][0] = 0.59754668912231692323e0;
+      v[1][4][1] = 0.17125249387868593878e0;
+      v[1][4][2] = 0.93606816359052444729e-1;
+      v[1][4][3] = 0.63728830247554475330e-1;
+      v[1][4][4] = 0.48187332620207367724e-1;
+      v[1][4][5] = 0.38708290797416359020e-1;
+      v[1][5][0] = 0.52527944036356840363e0;
+      v[1][5][1] = 0.14574366656617935708e0;
+      v[1][5][2] = 0.78997159795636003667e-1;
+      v[1][5][3] = 0.53620816423066464705e-1;
+      v[1][5][4] = 0.40487985967086264433e-1;
+      v[1][5][5] = 0.32498604596082509165e-1;
+      v[2][0][0] = 0.17627471740390860505e1;
+      v[2][0][1] = 0.11149535993427670134e1;
+      v[2][0][2] = 0.84975788287855432210e0;
+      v[2][0][3] = 0.69800109142265347419e0;
+      v[2][0][4] = 0.59754668912231692318e0;
+      v[2][0][5] = 0.52527944036356840362e0;
+      v[2][1][0] = 0.64779357469631903702e0;
+      v[2][1][1] = 0.37165119978092233782e0;
+      v[2][1][2] = 0.26566721237799340376e0;
+      v[2][1][3] = 0.20794647083778622835e0;
+      v[2][1][4] = 0.17125249387868593876e0;
+      v[2][1][5] = 0.14574366656617935708e0;
+      v[2][2][0] = 0.38259785823210634567e0;
+      v[2][2][1] = 0.21243947071963858053e0;
+      v[2][2][2] = 0.14884907827788122009e0;
+      v[2][2][3] = 0.11487965864809909845e0;
+      v[2][2][4] = 0.93606816359052444712e-1;
+      v[2][2][5] = 0.78997159795636003667e-1;
+      v[2][3][0] = 0.26915893322379450223e0;
+      v[2][3][1] = 0.14726379157404849572e0;
+      v[2][3][2] = 0.10231567218303765514e0;
+      v[2][3][3] = 0.78525390514866270835e-1;
+      v[2][3][4] = 0.63728830247554475311e-1;
+      v[2][3][5] = 0.53620816423066464702e-1;
+      v[2][4][0] = 0.20702239737104695572e0;
+      v[2][4][1] = 0.11236373700291582202e0;
+      v[2][4][2] = 0.77727703422280083352e-1;
+      v[2][4][3] = 0.59489228415223897563e-1;
+      v[2][4][4] = 0.48187332620207367713e-1;
+      v[2][4][5] = 0.40487985967086264434e-1;
+      v[2][5][0] = 0.16800109713227567468e0;
+      v[2][5][1] = 0.90737303111246235879e-1;
+      v[2][5][2] = 0.62605132021577676399e-1;
+      v[2][5][3] = 0.47838457013298217740e-1;
+      v[2][5][4] = 0.38708290797416359014e-1;
+      v[2][5][5] = 0.32498604596082509169e-1;
+      v[3][0][0] = 0.17627471740390860505e1;
+      v[3][0][1] = 0.11149535993427670134e1;
+      v[3][0][2] = 0.84975788287855432210e0;
+      v[3][0][3] = 0.69800109142265347419e0;
+      v[3][0][4] = 0.59754668912231692318e0;
+      v[3][0][5] = 0.52527944036356840362e0;
+      v[3][1][0] = 0.11149535993427670134e1;
+      v[3][1][1] = 0.74330239956184467563e0;
+      v[3][1][2] = 0.58409067050056091834e0;
+      v[3][1][3] = 0.49005462058486724584e0;
+      v[3][1][4] = 0.42629419524363098443e0;
+      v[3][1][5] = 0.37953577379738904654e0;
+      v[3][2][0] = 0.84975788287855432210e0;
+      v[3][2][1] = 0.58409067050056091834e0;
+      v[3][2][2] = 0.46727253640044873467e0;
+      v[3][2][3] = 0.39698780839518011595e0;
+      v[3][2][4] = 0.34864851772399749038e0;
+      v[3][2][5] = 0.31278926702684569312e0;
+      v[3][3][0] = 0.69800109142265347423e0;
+      v[3][3][1] = 0.49005462058486724586e0;
+      v[3][3][2] = 0.39698780839518011599e0;
+      v[3][3][3] = 0.34027526433872581371e0;
+      v[3][3][4] = 0.30088082631586196583e0;
+      v[3][3][5] = 0.27141910362887187844e0;
+      v[3][4][0] = 0.59754668912231692323e0;
+      v[3][4][1] = 0.42629419524363098445e0;
+      v[3][4][2] = 0.34864851772399749044e0;
+      v[3][4][3] = 0.30088082631586196576e0;
+      v[3][4][4] = 0.26744962339187730308e0;
+      v[3][4][5] = 0.24229245314748740295e0;
+      v[3][5][0] = 0.52527944036356840363e0;
+      v[3][5][1] = 0.37953577379738904655e0;
+      v[3][5][2] = 0.31278926702684569301e0;
+      v[3][5][3] = 0.27141910362887187862e0;
+      v[3][5][4] = 0.24229245314748740263e0;
+      v[3][5][5] = 0.22026586649771582089e0;
+    }
+  return v[vertex_index][i][j];
+}
+
+
 #endif