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17-Jul-2023 08:34:11

hexahedron_witherden_rule_test():
  MATLAB/Octave version 9.14.0.2206163 (R2023a)
  Test hexahedron_witherden_rule().

hexahedron_witherden_rule_test01():
  Quadrature rule for the unit hexahedron,
  Precision p = 5

     I      W          X           Y           Z

     1    0.110803    0.102089         0.5         0.5
     2    0.110803         0.5         0.5    0.897911
     3    0.110803         0.5    0.897911         0.5
     4    0.110803         0.5         0.5    0.102089
     5    0.110803    0.897911         0.5         0.5
     6    0.110803         0.5    0.102089         0.5
     7   0.0418975    0.879393    0.120607    0.120607
     8   0.0418975    0.120607    0.879393    0.879393
     9   0.0418975    0.120607    0.879393    0.120607
    10   0.0418975    0.120607    0.120607    0.120607
    11   0.0418975    0.120607    0.120607    0.879393
    12   0.0418975    0.879393    0.879393    0.120607
    13   0.0418975    0.879393    0.879393    0.879393
    14   0.0418975    0.879393    0.120607    0.879393

  Weight Sum    1

hexahedron_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit hexahedron.

  Stated precision of rule    = 5
  Number of quadrature points = 14

  Degree  Maximum error

   0     2.220446049250313e-16
   1     2.220446049250313e-16
   2     1.665334536937735e-16
   3     1.110223024625157e-16
   4     1.110223024625157e-16
   5     8.326672684688674e-17
   6     0.0004208754208754467
   7      0.001235269360269312

hexahedron_witherden_rule_test03():
  Test the precision of quadrature rules for the unit hexahedron.
  Check rules of precision p = 0 through 11
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error
   0                         0                         0
   1                         0                         0
   2     2.220446049250313e-16      3.33066907387547e-16
   3     2.220446049250313e-16      3.33066907387547e-16
   4     2.220446049250313e-16     6.661338147750939e-16
   5     2.220446049250313e-16     6.661338147750939e-16
   6     7.771561172376096e-16     7.771561172376096e-16
   7     7.771561172376096e-16     7.771561172376096e-16
   8     5.551115123125783e-17     5.551115123125783e-16
   9     5.551115123125783e-17     6.661338147750939e-16
  10     1.221245327087672e-15     2.220446049250313e-15
  11     1.221245327087672e-15     2.498001805406602e-15

hexahedron_witherden_rule_test():
  Normal end of execution.

17-Jul-2023 08:34:11