> Well, the question in my mind is: what happens with DG when the element is increased to the size of the complete flow domain (so we have one element) and the interpolation order is / > > > increased gradually. > Wouldn't DG in this case reduce to the basic Galerkin method, which is known to be unstable? Or is DG still guaranteed to give stable solutions?
A method with global test and trial functions is kind of a spectral method. Anyway depending on the formulation there are still significant differences. The way you impose boundary conditions might influence the accuracy and the stability of the method. If you weekly impose boundary conditions based on a dG formulation you will notice that Dirichlet boundary conditions might not be exactly satisfied. This reflects an insufficient spatial resolution and indicates the ability to distribute discretization errors on the boundary of the domain (one element). I mean that the error on the boundary is consistent with the discretization error inside the domain and, in my experience, this is not bad. Lorenzo On Fri, Apr 19, 2013 at 12:52 AM, Manav Bhatia <[email protected]>wrote: > > > On Apr 18, 2013, at 6:29 PM, Jed Brown <[email protected]> wrote: > > > lorenzo alessio botti <[email protected]> writes: > > > >> In my experience dG works without stabilization and additional > artificial > >> viscosity > > > > This is generally attributed to the cell entropy inequality. > > > > http://www.ams.org/journals/mcom/1994-62-206/S0025-5718-1994-1223232-7/ > > > > This is the best stability result I'm aware of for any high order linear > > spatial discretization. > > Well, the question in my mind is: what happens with DG when the element > is increased to the size of the complete flow domain (so we have one > element) and the interpolation order is increased gradually. > > Wouldn't DG in this case reduce to the basic Galerkin method, which is > known to be unstable? Or is DG still guaranteed to give stable solutions? > > Manav > > ------------------------------------------------------------------------------ Precog is a next-generation analytics platform capable of advanced analytics on semi-structured data. The platform includes APIs for building apps and a phenomenal toolset for data science. Developers can use our toolset for easy data analysis & visualization. Get a free account! http://www2.precog.com/precogplatform/slashdotnewsletter _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
