A finite-element approximation of anisotropic second order elliptic problems on a region, which is a union of rectangles, is discussed. The coefficients are piecewise constant on rectangular subregions of the original region. The additive Schwarz method (AMS) with minimal overlap for solving the resulting systems is described and analyzed. It uses three coarse spaces, standard and two special.
A rate of convergence of the method is of the order of (H/h)1/2 when cg is used. Here H and h are parameters of the coarse and fine triangulation. The rate of convergence of the method is independent of the coefficients, i.e. their discontinuity and anisotropy.
This is joint work with Petter Bjørstad.
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