Convergence rates for the coupling of FEM and collocation BEM

Abstract

We prove convergence of the coupling of finite and boundary elements where Galerkin's method is used for finite elements and collocation for boundary elements. We consider linear elliptic boundary value problems in two dimensions, in particular problems in elasticity. The mesh width k of the boundary elements and the mesh width h of the finite elements are required to satisfy k≤βh with suitable β. Asymptotic error estimates in the energy norm and in the L 2 norm are derived. Numerical examples are included.