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A projection-based error analysis of HDG methods
Author(s):
Bernardo
Cockburn;
Jayadeep
Gopalakrishnan;
Francisco-Javier
Sayas.
Journal:
Math. Comp.
79
(2010),
1351-1367.
MSC (2010):
Primary 65M60, 65N30, 35L65
Posted:
March 18, 2010
MathSciNet review:
2629996
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Additional information
Abstract:
We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG method applied to a model second-order elliptic problem.
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Additional Information:
Bernardo
Cockburn
Affiliation:
School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455
Email:
cockburn@math.umn.edu
Jayadeep
Gopalakrishnan
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611-8105
Email:
jayg@math.ufl.edu
Francisco-Javier
Sayas
Affiliation:
Departamento de Matemática Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain
Email:
sayas002@umn.edu
DOI:
10.1090/S0025-5718-10-02334-3
PII:
S 0025-5718(10)02334-3
Keywords:
Discontinuous Galerkin methods,
hybridization,
superconvergence,
postprocessing
Received by editor(s):
December 22, 2008
Received by editor(s) in revised form:
April 9, 2009
Posted:
March 18, 2010
Additional Notes:
The first author was supported in part by the National Science Foundation (Grant DMS-0712955) and by the University of Minnesota Supercomputing Institute
The second author was supported in part by the National Science Foundation under grants DMS-0713833 and SCREMS-0619080.
The third author was partially supported by MEC/FEDER Project MTM2007-63204, Gobierno de Aragón (Grupo PDIE) and was a Visiting Professor of the School of Mathematics, University of Minnesota, during the development of this work.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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