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Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. (English) Zbl 0884.65119

Second order elliptic problems are solved using the simple nonconforming approximation simultaneously with the two-level domain decomposition method. For this iterative method the bound for the condition number grows only logarithmically with respect to the number of degrees of freedom in each subregion of the problem. This bound holds for two and three dimensions and is independent of jumps in the values of the coefficients and the number of subregions. The author introduces face coarse spaces and isomorphisms to construct the appropriate mapping between conforming and nonconforming spaces.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F35 Numerical computation of matrix norms, conditioning, scaling
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