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A projection-based error analysis of HDG methods

Authors: Bernardo Cockburn, Jayadeep Gopalakrishnan and Francisco-Javier Sayas
Journal: Math. Comp. 79 (2010), 1351-1367
MSC (2010): Primary 65M60, 65N30, 35L65
Published electronically: March 18, 2010
MathSciNet review: 2629996
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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

Jayadeep Gopalakrishnan
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611–8105

Francisco-Javier Sayas
Affiliation: Departamento de Matemática Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain

Keywords: Discontinuous Galerkin methods, hybridization, superconvergence, postprocessing
Received by editor(s): December 22, 2008
Received by editor(s) in revised form: April 9, 2009
Published electronically: 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.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.