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Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations

Authors: Erik Burman and Alexandre Ern
Journal: Math. Comp. 76 (2007), 1119-1140
MSC (2000): Primary 65N30, 65N12, 65N15, 65D05, 65N35
Published electronically: January 24, 2007
MathSciNet review: 2299768
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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.

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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

Alexandre Ern
Affiliation: CERMICS, Ecole des Ponts, ParisTech, Champs-sur-Marne, 77455 Marne la Vallée, Cedex 2, France
MR Author ID: 349433

Keywords: Continuous interior penalty, $hp$-finite element method, convection-diffusion, $hp$-interpolation and projection, $hp$-inverse trace inequality
Received by editor(s): January 24, 2005
Received by editor(s) in revised form: March 25, 2006
Published electronically: January 24, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.