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A new error analysis for discontinuous finite element methods for linear elliptic problems


Author: Thirupathi Gudi
Journal: Math. Comp. 79 (2010), 2169-2189
MSC (2010): Primary 65N30, 65N15
Published electronically: April 12, 2010
MathSciNet review: 2684360
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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$.


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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

DOI: https://doi.org/10.1090/S0025-5718-10-02360-4
Keywords: Optimal error estimates, elliptic regularity, finite element, discontinuous Galerkin, nonconforming
Received by editor(s): January 5, 2009
Received by editor(s) in revised form: June 16, 2009
Published electronically: April 12, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.