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

Saturday, January 25th, 1997

Optimal error estimates and multiscale applications

In a model case of an elliptic equation with periodic boundary conditions (or with Dirichlet boundary conditions and cell symmetry) we prove an optimal energy estimate where the right hand side is measured in the L_2-norm. This is transfered to discrete approximations yielding for example convergence of a two-grid scheme for solving the arising linear system. We briefly discuss 'ideal' approximations with adapted function spaces and connections to algebraic multigrid theory.