Mortar finite element methods for discontinuous coefficients

In this paper, we consider a mortar finite element method for second order elliptic boundary value problems with discontinuous coefficients. At the in terface where the coefficient is discontinuous, different triangulations an d/or discretizations are coupled by means of Lagrange multipliers. The nume rical algorithm is based on the algebraic saddle point formulation. The cou pling of P1 conforming finite elements with P1 conforming and nonconforming Crouzeix-Raviart elements is studied. Finally, we present the performance of the adaptive refinement process.