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

Friday, January 24th, 1997

Composite Finite Elements for coarse-level discretizations of PDEs with essential boundary conditions

Composite Finite Elements allow coarse-level discretizations of PDEs where the minimal number of degrees of freedom is independent of the number of micro-structures of the problem (geometric details, oscillating coefficients, etc). We can prove that, for this new finite element space, the approximation property is valid also for the very coarse-level discretizations. In our talk, we will focus on the treatment of essential boundary conditions. For this purpose, we will use prolongation operators which are stable in H^1, are defined locally, and preserve the essential boundary conditions.