From: Wolfgang Bangerth Date: Mon, 6 Apr 1998 17:32:41 +0000 (+0000) Subject: Add comment about quadrature rules. X-Git-Tag: v8.0.0~23105 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=10b47925292b9d647a1522041f6aa58b9f1ef73e;p=dealii.git Add comment about quadrature rules. git-svn-id: https://svn.dealii.org/trunk@149 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/deal.II/include/numerics/base.h b/deal.II/deal.II/include/numerics/base.h index 4a716bb56d..6b5bb8ea2e 100644 --- a/deal.II/deal.II/include/numerics/base.h +++ b/deal.II/deal.II/include/numerics/base.h @@ -171,9 +171,9 @@ enum NormType { is the same as a #cell_iterator# takes when started with #begin_active# and promoted with the #++# operator. - You can use the #distribute_cell_to_dof_vector# function to convert cell - based data to a data vector with values on the degrees of freedom, which - can then be attached to a #DataOut# object to be printed. + You can use the #distribute_cell_to_dof_vector# function of the #DoFHandler# + class to convert cell based data to a data vector with values on the degrees + of freedom, which can then be attached to a #DataOut# object to be printed. Presently, there is the possibility to compute the following values from the difference, on each cell: #mean#, #L1_norm#, #L2_norm#, #Linfty_norm#. @@ -187,6 +187,17 @@ enum NormType { not evaluate the difference at the end or corner points of the cells. You may want to chose a quadrature formula with more quadrature points or one with another distribution of the quadrature points in this case. + You should also take into account the superconvergence properties of finite + elements in some points: for example in 1D, the standard finite element + method is a collocation method and should return the exact value at nodal + points. Therefore, the trapezoidal rule should always return a vanishing + L-infinity error. Conversely, in 2D the maximum L-infinity error should + be located at the vertices or at the center of the cell, which would make + it plausible to use the Simpson quadrature rule. On the other hand, there + may be superconvergence at Gauss integration points. These examples are not + intended as a rule of thumb, rather they are though to illustrate that the + use of the wrong quadrature formula may show a significantly wrong result + and care should be taken to chose the right formula. To get the {\it global} L_1 error, you have to sum up the entries in #difference#, e.g. using the STL function