Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Sunday, January 26th, 1997

The additive Schwarz method for finite element anisotropic elliptic problems

A finite element approximation of anisotropic second order elliptic problems on a rectangular region 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)^\frac{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.