Preprint A456/2006
A Neumann-Neumann method for DG discretization of elliptic problems
Maksymilian Dryja | Marcus Sarkis
Keywords: interior penalty discretization | discontinuous Galerkin method | elliptic problems with discontinuous coefficients | finite element method | Neumann-Neumann algorithms | Schwarz methods | preconditioners

A discontinuous Galerkin (DG) discretization of Dirichlet problem for second order elliptic equations with discontinuous coefficients in the 2-D is considered. For this discretization, a Neumann-Neumann (N-N) algorithm is designed and analyzed as an additive Schwarz method (ASM). The coarse spaces is defined usinga special partition of unity. The method is almost optimal under the natural assumption on the triangulation. Its rate of convergence is independent of jumps of coefficients. The method is well suited for parallel computations.