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Adaptive FE–BE coupling for an electromagnetic problem in ℝ 3 —A residual error estimator
Author(s) -
Leydecker Florian,
Maischak Matthias,
Stephan Ernst P.,
Teltscher Matthias
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1389
Subject(s) - mathematics , estimator , piecewise , boundary (topology) , galerkin method , mathematical analysis , helmholtz equation , residual , domain decomposition methods , boundary value problem , finite element method , algorithm , statistics , physics , thermodynamics
We construct a reliable and efficient residual‐based local a posteriori error estimator for a Galerkin method coupling finite elements and boundary elements for an eddy current problem in a three‐dimensional polyhedral domain. For the proof of the efficiency of the error estimator, we assume that the boundary mesh is quasi‐uniform and that the boundary surface and the boundary data satisfy certain smoothness assumptions. The Galerkin method uses lowest‐order Nédélec elements in the interior domain and vectorial surface rotations of continuous, piecewise bilinear functions on the boundary. Singular, weakly singular and hypersingular boundary integral operators appearing in the variational formulation show up in terms of the error estimator as well. The estimator is derived from the defect equation using a Helmholtz decomposition and Green's formulas. The decomposed parts of the Galerkin error are approximated by local interpolation operators. Numerical tests underline reliability and efficiency of the residual error estimator. Copyright © 2010 John Wiley & Sons, Ltd.