Composite finite elements for elliptic interface problems

Abstract

A Composite Finite Element method approximates linear elliptic boundary value problems with discontinuous diffusion coefficient at possibly high contrast. The discontinuity appears at some interface that is not necessarily resolved by the underlying finite element mesh. The method is non-conforming in the sense that shape functions preserve continuity across the interface in only an approximate way. However, the method allows balancing this non-conformity error and the error of the best approximation in such a way that the total discretization error (in energy norm) decreases linear with regard to the mesh size and independent of contrast.