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
DOI:
https://doi.org/10.1090/S0025-5718-07-01951-5
Published electronically:
January 24, 2007
MathSciNet review:
2299768
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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
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.