Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
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- by Erik Burman and Alexandre Ern PDF
- Math. Comp. 76 (2007), 1119-1140 Request permission
Abstract:
A continuous interior penalty $hp$-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an $hp$-inverse trace inequality, a local discontinuous to continuous $hp$-interpolation result, and $hp$-error estimates for continuous $L^2$-orthogonal projections.References
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Additional Information
- Erik Burman
- Affiliation: Institut d’Analyse et Calcul Scientifique (CMCS/IACS), Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland
- MR Author ID: 602430
- Email: Erik.Burman@epfl.ch
- Alexandre Ern
- Affiliation: CERMICS, Ecole des Ponts, ParisTech, Champs-sur-Marne, 77455 Marne la Vallée, Cedex 2, France
- MR Author ID: 349433
- Email: ern@cermics.enpc.fr
- Received by editor(s): January 24, 2005
- Received by editor(s) in revised form: March 25, 2006
- Published electronically: January 24, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1119-1140
- MSC (2000): Primary 65N30, 65N12, 65N15, 65D05, 65N35
- DOI: https://doi.org/10.1090/S0025-5718-07-01951-5
- MathSciNet review: 2299768