COUPLING OF FINITE AND BOUNDARY ELEMENT METHODS FOR AN ELASTOPLASTIC INTERFACE PROBLEM

A class of transmission problems is considered in which a nonlinear variational problem in one domain is coupled with a linear elliptic problem in a second domain. A typical example is a problem from three-dimensional elasticity theory where an elastoplastic material is embedded into a linear elastic material. The nonlinear problem is given in variational form with a strictly convex functional. The linear elliptic problem is described by boundary integral equations on the coupling boundary. The typical saddle point structure of such problems is analyzed. Galerkin approximations are studied which consist of a finite element approximation in the first domain coupled with a boundary element method on the coupling boundary. The convergence of the Galerkin approximation is based on the saddle-point structure which is shown to hold for the exact as well as the discretized problems.