A FETI-DP PRECONDITIONER FOR A COMPOSITE FINITE ELEMENT AND DISCONTINUOUS GALERKIN METHOD

In this paper a Nitsche-type discretization based on a discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region Omega which is a union of N disjoint polygonal subdomains Omega(i) of diameter O(H-i). The discontinuities of the coefficients, possibly very large, are assumed to occur only across the subdomain interfaces. partial derivative Omega(i). Inside each subdomain, a conforming finite element space on a quasi-uniform triangulation with mesh size O(h(i)) is introduced. To handle the nonmatching meshes across the subdomain interfaces, a DG 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 + max(i) log H-i/h(i))(2) with a constant C independent of h(i), h(i)/h(j), H-i 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.