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Media type:
E-Book
Title:
Neumann-Neumann methods for a DG discretization of elliptic problems with discontinous coefficients on geometrically nonconforming substructures
Description:
discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest is assumed to be a union of polygonal substructures i of size O(Hi). We allow this substructure decomposition to be geometrically nonconforming. Inside each substructure i, a conforming finite element space associated to a triangulation Thi( i) is introduced. To handle the nonmatching meshes across i, a discontinuous Galerkin discretization is considered. In this paper additive and hybrid Neumann-Neumann Schwarz methods are designed and analyzed. Under natural assumptions on the coefficients and on the mesh sizes across @ i, a condition number estimate C(1 + maxi log Hi hi)2 is established with C independent of hi, Hi, hi/hj , and the jumps of the coefficients. The method is well suited for parallel computations and can be straightforwardly extended to three dimensional problems. Numerical results are included.