Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
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- by Ralf Hiptmair, Andrea Moiola and Ilaria Perugia PDF
- Math. Comp. 82 (2013), 247-268 Request permission
Abstract:
In this paper, we extend to the time-harmonic Maxwell equations the $p$–version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.References
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Additional Information
- Ralf Hiptmair
- Affiliation: Seminar for Applied Mathematics, ETH Zürich, 8092 Zürich, Switzerland
- Email: ralf.hiptmair@sam.math.ethz.ch
- Andrea Moiola
- Affiliation: Seminar for Applied Mathematics, ETH Zürich, 8092 Zürich, Switzerland
- Address at time of publication: Department of Mathematics and Statistics, University of Reading,Whiteknights, P.O. Box 220, Reading RG6 6AX, UK
- Email: andrea.moiola@sam.math.ethz.ch
- Ilaria Perugia
- Affiliation: Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy
- MR Author ID: 366660
- Email: ilaria.perugia@unipv.it
- Received by editor(s): February 21, 2011
- Received by editor(s) in revised form: September 3, 2011
- Published electronically: July 3, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 247-268
- MSC (2010): Primary 65N15, 65N30, 35Q61
- DOI: https://doi.org/10.1090/S0025-5718-2012-02627-5
- MathSciNet review: 2983024