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http://dx.doi.org/10.12941/jksiam.2013.17.139

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)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.17, no.3, 2013 , pp. 139-170 More about this Journal
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.
Keywords
hierarchical based a posteriori error estimation; Maxwell's equations; eddy currents; fem-bem coupling; N$\acute{e}$d$\acute{e}$lec's elements; Raviart-Thomas elements;
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