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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Email: Erik.Burman@epfl.ch

Alexandre Ern
Affiliation: CERMICS, Ecole des Ponts, ParisTech, Champs-sur-Marne, 77455 Marne la Vallée, Cedex 2, France
Email: ern@cermics.enpc.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01951-5
PII: S 0025-5718(07)01951-5
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.