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Continuous interior penalty  -finite element methods for advection and advection-diffusion equations
Author(s):
Erik
Burman;
Alexandre
Ern.
Journal:
Math. Comp.
76
(2007),
1119-1140.
MSC (2000):
Primary 65N30, 65N12, 65N15, 65D05, 65N35
Posted:
January 24, 2007
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Additional information
Abstract:
A continuous interior penalty  -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  -inverse trace inequality, a local discontinuous to continuous  -interpolation result, and  -error estimates for continuous  -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:
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
Posted:
January 24, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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