Mixed enrichment for the finite element method in heterogeneous media

Problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media. These problems are usually very demanding in terms of computations with the conventional finite element method. On the other hand dierent enriched finite element methods such as the partition of unity which proved to be very successful in treating similar problems, are developed and studied for homogeneous media. In this work we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials. The idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method. Although presented within the partition of unity context the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials.