A FETI-DP Preconditioner for a Composite Finite Element and Discontinuous Galerkin Method

In this paper a Nitsche-type discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region Ω which is a union of N disjoint polygonal subdomains Ωi of diameter O(Hi). The discontinuities of the coefficients, possibly very large, are assumed to occur only across the subdomain interfaces ∂Ωi. Inside each subdomain, a conforming finite element space on a quasiuniform triangulation with mesh size O(hi) is introduced. To handle the nonmatching meshes across the subdomain interfaces, a discontinuous Galerkin discretization is applied only on the interfaces. For solving the resulting discrete system, a FETI-DP type method is proposed and analyzed. It is established that the condition number of the preconditioned linear system is estimated by C(1 +maxi logHi/hi) 2 with a constant C independent of hi, hi/hj , Hi 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 validade the theory.