Multilevel discontinuous Galerkin methods on locally refined meshes

Guido Kanschat

Email: kanschat@math.tamu.edu
Postal address: Texas A&M University Department of Mathematics, 3368 TAMU, College Station, TX 77843-3368

On hierarchical meshes generated by local refinement of a coarse mesh, a multilevel method must be devised carefully in order to maintain optimal  omplexity. Here, we show that the scheme involving local smoothing is particularly suited for discontinuous Galerkin discretizations of elliptic operators. While the efficiency of the method exhibits independence of the refinement pattern of the grid, the method can still be implemented in a general way. Results will be shown for the interior penalty method as well as for an extension to the LDG method.