A P-HIERARCHICAL ERROR ESTIMATOR FOR A FEM-BEM COUPLING OF AN EDDY CURRENT PROBLEM IN R 3

Abstract

We extend a p-hierarchical decomposition of the second degree finite element space of Nedelec for tetrahedral meshes in three dimensions given in [1] to meshes with hexahedral elements, and derive p-hierarchical decompositions of the second degree finite element space of Raviart-Thomas in two dimensions for triangular and quadrilateral meshes. After having proved stability of these subspace decompositions and requiring certain saturation assumptions to hold, we construct a local a posteriori error estimator for fem and bem coupling of a time-harmonic electromagnetic eddy current problem in R 3 . We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.