Details
| Original language | English |
|---|---|
| Pages (from-to) | 2162-2186 |
| Number of pages | 25 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 33 |
| Issue number | 18 |
| Early online date | 7 Oct 2010 |
| Publication status | Published - 1 Dec 2010 |
Abstract
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.
Keywords
- eddy currents, FE-BE coupling, Maxwell's equations, residual based a posteriori error estimation
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Engineering(all)
- General Engineering
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In: Mathematical Methods in the Applied Sciences, Vol. 33, No. 18, 01.12.2010, p. 2162-2186.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive FE-BE coupling for an electromagnetic problem in ℝ3
T2 - A residual error estimator
AU - Leydecker, Florian
AU - Maischak, Matthias
AU - Stephan, Ernst P.
AU - Teltscher, Matthias
PY - 2010/12/1
Y1 - 2010/12/1
N2 - 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.
AB - 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.
KW - eddy currents
KW - FE-BE coupling
KW - Maxwell's equations
KW - residual based a posteriori error estimation
UR - http://www.scopus.com/inward/record.url?scp=78650088629&partnerID=8YFLogxK
U2 - 10.1002/mma.1389
DO - 10.1002/mma.1389
M3 - Article
AN - SCOPUS:78650088629
VL - 33
SP - 2162
EP - 2186
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 18
ER -