Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems

  1. Raytcho Lazarov1,
  2. Sergey Repin2,
  3. Satyendra K. Tomar3,*

Article first published online: 29 AUG 2008

DOI: 10.1002/num.20386

Issue

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations

Volume 25, Issue 4, pages 952–971, July 2009

Additional Information

How to Cite

Lazarov, R., Repin, S. and Tomar, S. K. (2009), Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems. Numerical Methods for Partial Differential Equations, 25: 952–971. doi: 10.1002/num.20386

Author Information

  1. 1

    Department of Mathematics, Texas A&M University, College Station, Texas 77843

  2. 2

    Laboratory of Mathematical Physics Petersburg, Department of Steklov Institute of Mathematics 27, Fontanka, 191011, St. Petersburg, Russia

  3. 3

    Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, A-4040 Linz, Austria

*Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, A-4040 Linz, Austria

Publication History

  1. Issue published online: 20 APR 2009
  2. Article first published online: 29 AUG 2008
  3. Manuscript Accepted: 3 JUN 2008
  4. Manuscript Received: 14 FEB 2007

Funded by

  • NSF. Grant Number: DMS-0713829
  • Austrain Academy of Sciences

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Keywords:

  • a posteriori error estimates;
  • discontinuous Galerkin method;
  • nonconforming approximations

Abstract

In this article, we develop functional a posteriori error estimates for discontinuous Galerkin (DG) approximations of elliptic boundary-value problems. These estimates are based on a certain projection of DG approximations to the respective energy space and functional a posteriori estimates for conforming approximations developed by S. Repin (see e.g., Math Comp 69 (2000) 481–500). On these grounds, we derive two-sided guaranteed and computable bounds for the errors in “broken” energy norms. A series of numerical examples presented confirm the efficiency of the estimates. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

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