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DOI QR Code

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

  • Leydecker, Florian (INSTITUTE FOR APPLIED MATHEMATICS, LEIBNIZ UNIVERSITAT HANNOVER) ;
  • Maischak, Matthias (BRUNEL UNIVERSITY) ;
  • Stephan, Ernst P. (INSTITUTE FOR APPLIED MATHEMATICS, LEIBNIZ UNIVERSITAT HANNOVER) ;
  • Teltscher, Matthias (INSTITUTE FOR APPLIED MATHEMATICS, LEIBNIZ UNIVERSITAT HANNOVER)
  • Received : 2011.08.24
  • Accepted : 2013.04.30
  • Published : 2013.09.25

Abstract

We extend a p-hierarchical decomposition of the second degree finite element space of N$\acute{e}$d$\acute{e}$lec 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 $\mathbb{R}^3$. We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.

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