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

 

Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities


Authors: Sebastian Franz, R. Bruce Kellogg and Martin Stynes
Journal: Math. Comp. 81 (2012), 661-685
MSC (2010): Primary 65N30
Published electronically: July 20, 2011
MathSciNet review: 2869032
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Abstract: An error analysis of Galerkin and streamline diffusion finite element methods for the numerical solution of a singularly perturbed convection-diffusion problem is given. The problem domain is the unit square. The solution contains boundary layers and corner singularities. A tensor product Shishkin mesh is used, with piecewise bilinear trial functions. The error bounds are uniform in the singular perturbation parameter. Numerical results supporting the theory are given.


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Additional Information

Sebastian Franz
Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
Email: sebastian.franz@ul.ie

R. Bruce Kellogg
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: bklandrum@gmail.com

Martin Stynes
Affiliation: Department of Mathematics, National University of Ireland, Cork, Ireland
Email: m.stynes@ucc.ie

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02526-3
PII: S 0025-5718(2011)02526-3
Received by editor(s): September 3, 2009
Received by editor(s) in revised form: November 2, 2010, and January 25, 2011
Published electronically: July 20, 2011
Additional Notes: The research of the first author was supported by Science Foundation Ireland under the Research Frontiers Programme 2008; Grant 08/RFP/MTH1536
The research of the second author was supported by the Boole Centre for Research in Informatics at National University of Ireland, Cork
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.