FETI-DP method for DG discretization of elliptic problems with discontinuous coefficients
Marcus Sarkis | Dryja, Maksymilian
interior penalty discretization | discontinuous Galerkin | elliptic problems with discontinuous coefficients. finite element method | FETI-DP algorithms | preconditioners
In this paper a discontinuous Galerkin (DG) discretization of an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region $\Omega$ which is a union of disjoint polygonals $\Omega_i$ of diameter $O(H_i)$ and forms a geometrically conforming partition of $\Omega$. The discontinuities of the coefficients are assumed to occur only across $\partial \Omega_i$. Inside of each substructure $\Omega_i$, a conforming finite element space on a quasiuniform triangulation with triangular elements and mesh size $O(h_i)$ is introduced. To handle the nonmatching meshes across $\partial \Omega_i$, a discontinuous Galerkin discretization is considered. For solving the resulting discrete problem, a FETI-DP method is designed and analyzed. It is established that the condition number of the method is estimated by $C(1 + \max_i \log H_i/h_i)^2$ with a constant $C$ independent of $h_i$, $H_i$ and the jumps of the coefficients. The method is well suited for parallel computations and it can be straightforwardly extended to three-dimensional problems.