Dear Jaekwang, The role of the additional quadrature formula is to ensure that your function is not evaluated at "superconvergent" points, which would lead to an underestimation in the error associated with the finite element solution. I have little knowledge of functional analysis, so apart from directing you to the "detailed description <https://www.dealii.org/developer/doxygen/deal.II/namespaceVectorTools.html>" of the VectorTools namespace, where it is stated that
there may be superconvergence at Gauss integration points I can't offer you any more insight (although perhaps someone else will). In the mean time, I would suggest reading the entire introduction written for the VectorTools namespace to see if you can gain some further information from it. Regards, Jean-Paul On Friday, November 11, 2016 at 5:19:58 PM UTC+1, Jaekwang Kim wrote: > > Hi, all. > I have a question on how 'VectorTools::integrate_difference' works > > const MappingQ<dim> mapping (degree); > > > > VectorTools::integrate_difference (mapping, > dof_handler,solution,Solution<dim>(), > > > difference_per_cell,QGauss<dim>(degree+2),VectorTools::L2_norm); > > > const double L2_error = difference_per_cell.l2_norm(); > > > I use this function, to compare my numerical solution with exact solution > which is continuous function. > > > If I have numerical solution, > > In cell-wise, I have node values of numerical solution at each dof point. > (Quadrature Point) - I think that dof_handler has all of this information > already. > > So, I think I don't need to generate new quadrature points to integrate my > numerical solution. > > In a same way, I think I can use same quadrature points to integrate > continuous function. > > > But the function ask me a input of which guadrature to use to integrate > this .......I don't understand where do we need this quadrature... > > what is the role of 6th argument of this function ? > > > QGauss<dim>(degree+2) > > > Thank you always ! > > > Jaekwang Kim > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
