Mortar finite elements for coupling compressible and nearly incompressible materials in elasticity

We consider the coupling of compressible and nearly incompressible materials within the framework of mortar methods. Taking into account the locking effect, we use a suitable discretization for the nearly incompressible material and work with a standard conforming discretization elsewhere. The coupling of different discretization schemes in different subdomains are handled by flexible mortar techniques. A priori error analysisis carried out for the coupled problem, and several numerical examples are presented. Using dual Lagrange multipliers, the Lagrange multipliers can easily be eliminated by local static condensation.