Numerical homogenization for indefinite H(curl)-problems

Verfürth, Barbara

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 137-146

Abstract

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In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we extend the procedure of [D. Gallistl, P. Henning, B. Verfürth, Numerical homogenization for H(curl)-problems, arXiv:1706.02966, 2017] to the case of indefinite problems. In particular, this requires a careful analysis of the well-posedness of the corrector problems as well as the numerical homogenization scheme.

How to cite

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Verfürth, Barbara. "Numerical homogenization for indefinite H(curl)-problems." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 137-146. <http://eudml.org/doc/294915>.

@inProceedings{Verfürth2017,
abstract = {In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we extend the procedure of [D. Gallistl, P. Henning, B. Verfürth, Numerical homogenization for H(curl)-problems, arXiv:1706.02966, 2017] to the case of indefinite problems. In particular, this requires a careful analysis of the well-posedness of the corrector problems as well as the numerical homogenization scheme.},
author = {Verfürth, Barbara},
booktitle = {Proceedings of Equadiff 14},
keywords = {Multiscale method, wave propagation, Maxwell’s equations, finite element method},
location = {Bratislava},
pages = {137-146},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Numerical homogenization for indefinite H(curl)-problems},
url = {http://eudml.org/doc/294915},
year = {2017},
}

TY - CLSWK
AU - Verfürth, Barbara
TI - Numerical homogenization for indefinite H(curl)-problems
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 137
EP - 146
AB - In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we extend the procedure of [D. Gallistl, P. Henning, B. Verfürth, Numerical homogenization for H(curl)-problems, arXiv:1706.02966, 2017] to the case of indefinite problems. In particular, this requires a careful analysis of the well-posedness of the corrector problems as well as the numerical homogenization scheme.
KW - Multiscale method, wave propagation, Maxwell’s equations, finite element method
UR - http://eudml.org/doc/294915
ER -

References

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