Composite Finite Elements for Discrete Homogenization

Stefan Sauter

Institute for Applied Mathematics University Kiel, D-24098 Kiel, FRG.

Abstract

In our talk we will present a new class of finite elements called ”Composite Finite Elements”. They are developed for the discretization of PDEs containing small mirco-strucutres as, e.g., rough boundaries or highly varying coefficients. The minimal number of unknowns where the approximation porperty starts is independent of the microstructures. Hence, Composite Finite Elements can be used preferably in combination with multi-grid methods for contructing coarse grid operators. A further application is the (discrete) homogenization of PDEs for non-periodic problems. In our talk we will focus on the modeling of boundary conditions and illustrate the theory by numerical results.