Journal of the Korean Society for Industrial and Applied Mathematics

  • 제17권3호
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  • Pages.139-170
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  • 2013
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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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)
  • 투고 : 2011.08.24
  • 심사 : 2013.04.30
  • 발행 : 2013.09.25
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초록

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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참고문헌

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