Exponential convergence of hp-FEM for Maxwell\'s equations with weighted regularization in polygonal domains
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Date
2004-06Type
- Report
ETH Bibliography
yes
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Abstract
The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic
problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the
regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h Version of Finite Elements, [20]. We prove
exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these
axioms for several specific families of hp finite element spaces. Show more
Publication status
unpublishedJournal / series
Research ReportVolume
Publisher
ETH Zürich, Seminar für Angewandte MathematikOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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