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

Saturday, January 25th, 1997

Robust iterative methods by interface reduction for solving highly anisotropic elliptic equations

We propose and analyze the robust and asymptotically optimal iterative method for solving an interface reduction to anisotropic elliptic equations with piecewise constant coefficients, where the direction of anisotropic behaviour may change within a domain. Jumps of anisotropy coefficients align with the coarse mesh decomposition. The construction is essentially based on using of an exotic nonconformal coarse mesh space which resolves qualitatively the interior boundary layers near the interface. Our method extends the familiar Bramble-Pasciak-Schatz preconditioner to the case of highly anisotropic equations. Under certain assumptions on the diffusion coefficients behaviour, a stable multilevel method is cosidered to solve the underlying coarse mesh problem. The results of numerical experiments are presented.