A new error analysis for discontinuous finite element methods for linear elliptic problems
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Abstract:
The standard a priori error analysis of discontinuous Galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the Galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm. In this paper, a new error analysis of discontinuous Galerkin methods is developed using only the $H^k$ weak formulation of a boundary value problem of order $2k$. This is accomplished by replacing the Galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in $H^k$.References
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Additional Information
- Thirupathi Gudi
- Affiliation: Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: tgudi@cct.lsu.edu
- Received by editor(s): January 5, 2009
- Received by editor(s) in revised form: June 16, 2009
- Published electronically: April 12, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 2169-2189
- MSC (2010): Primary 65N30, 65N15
- DOI: https://doi.org/10.1090/S0025-5718-10-02360-4
- MathSciNet review: 2684360