Description:
In this paper a discontinuous Galerkin (DG) discretization of an elliptic twodimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region which is a union of disjoint polygonals i of diameter O(Hi) and forms a geometrically conforming partition of The discontinuities of the coefficients are assumed to occur only across i. Inside of each substructure i, a conforming finite element space on a quasiuniform triangulation with triangular elements and mesh size O(hi) is introduced. To handle the nonmatching meshes across @ 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 +maxi logHi/hi)2 with a constant C independent of hi, Hi and the jumps of the coefficients. The method is well suited for parallel computations and it can bestraightforwardly extended to three-dimensional problems