ON THE ADAPTIVE COUPLING OF FEM AND BEM IN 2-D-ELASTICITY

This paper concerns the combination of the finite element method (FEM) and the boundary element method (BEM) using the symmetric coupling. A s a model problem in two dimensions we consider the Hencky material (a certain nonlinear elastic material) in a bounded domain with Navier-L ame differential equation in the unbounded complementary domain. Using some boundary integral operators the problem is rewritten such that t he Galerkin procedure leads to a FEM/BEM coupling and quasi-optimally convergent discrete solutions. Beside this a priori information we der ive an a posteriori error estimate which allows (up to a constant fact or) the error control in the energy norm. Since information about the singularities of the solution is not available a priori in many situat ion and having in mind the goal of an automatic mesh-refinement we sta te adaptive algorithms for the h-version of the FEM/BEM-coupling. Illu strating numerical results are included.