Adaptive FE-BE coupling for an electromagnetic problem in ?~3 - A residual error estimator

摘要

We construct a reliable and efficient residual-based local a posteriori error estimator for a Galerkin method coupling finite elements and boundary elements for an eddy current problem in a three-dimensional polyhedral domain. For the proof of the efficiency of the error estimator, we assume that the boundary mesh is quasi-uniform and that the boundary surface and the boundary data satisfy certain smoothness assumptions. The Galerkin method uses lowest-order Nédélec elements in the interior domain and vectorial surface rotations of continuous, piecewise bilinear functions on the boundary. Singular, weakly singular and hypersingular boundary integral operators appearing in the variational formulation show up in terms of the error estimator as well. The estimator is derived from the defect equation using a Helmholtz decomposition and Green's formulas. The decomposed parts of the Galerkin error are approximated by local interpolation operators. Numerical tests underline reliability and efficiency of the residual error estimator.