Adaptive FEM-BEM coupling with a Schur complement error indicator
An interface problem in two dimensions with and inhomogeneous partial differential equation in the interior domain and a homogeneous partial differential equation in the exterior domain is considered. A symmetric coupling method and a Galerkin scheme are applied which yield a coupled set of finite element-boundary element equations. The Steklov-Poincaré operator is discretized using stable hierarchical basis decompositions for finite elements. It is shown that the two-level additive Schwarz operator has a bounded condition number. An a posteriori error estimate is derived with local error indicators. An adaptive algorithm to compute the finite element solution on a sequence of locally refined meshes in the interior domain and on the interface boundary is also presented. Finally, numerical experiments of a nonlinear interface problem in a L-shaped domain illustrate the reliability of the error indicators.
scientific article; zbMATH DE number 5726717