A projection-based error analysis of HDG methods
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- by Bernardo Cockburn, Jayadeep Gopalakrishnan and Francisco-Javier Sayas HTML | PDF
- Math. Comp. 79 (2010), 1351-1367 Request permission
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.References
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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
- MR Author ID: 661361
- Email: jayg@math.ufl.edu
- Francisco-Javier Sayas
- Affiliation: Departamento de Matemática Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain
- MR Author ID: 621885
- Email: sayas002@umn.edu
- 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. - © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 1351-1367
- MSC (2010): Primary 65M60, 65N30, 35L65
- DOI: https://doi.org/10.1090/S0025-5718-10-02334-3
- MathSciNet review: 2629996