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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.

journal of the korea society for industrial and applied mathematics

A P-HIERARCHICAL ERROR ESTIMATOR FOR A FEM-BEM COUPLING OF AN EDDY CURRENT PROBLEM IN ℝ<sup>3</sup>-DEDICATED TO PROFESSOR WOLFGANG L. WENDLAND ON THE OCCASION OF HIS 75TH BIRTHDAY

A P-HIERARCHICAL ERROR ESTIMATOR FOR A FEM-BEM COUPLING OF AN EDDY CURRENT PROBLEM IN ℝ3-DEDICATED TO PROFESSOR WOLFGANG L. WENDLAND ON THE OCCASION OF HIS 75TH BIRTHDAY

A P-HIERARCHICAL ERROR ESTIMATOR FOR A FEM-BEM COUPLING OF AN EDDY CURRENT PROBLEM IN ℝ³-DEDICATED TO PROFESSOR WOLFGANG L. WENDLAND ON THE OCCASION OF HIS 75TH BIRTHDAY