The analysis of a FETI-DP preconditioner for a full DG discretization of elliptic problems in two dimensions

摘要

In this paper a discretization based on a discontinuous Galerkin (DG) method for elliptic two-dimensional problems with discontinuous coefficients is considered. The problems are posed on a polygonal region which is a union of disjoint polygonal subdomains of diameter . The discontinuities of the coefficients, possibly very large, are assumed to occur only across the subdomain interfaces . In each a conforming quasi-uniform triangulation with parameters is constructed. We assume that the resulting triangulation in is also conforming, i.e., the meshes are assumed to match across the subdomain interfaces. On the fine triangulation, the problems are discretized by a DG method. For solving the resulting discrete systems, a FETI-DP type method is proposed and analyzed. It is established that the condition number of the preconditioned linear system is estimated by with a constant independent of , and the jumps of coefficients. The method is well suited for parallel computations and it can be extended to three-dimensional problems. Numerical results are presented to validate the theory.