Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
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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.
Numerical Methods for Partial Differential Equations
author list (cited authors)
Lazarov, R., Repin, S., & Tomar, S. K.
complete list of authors
Lazarov, Raytcho||Repin, Sergey||Tomar, Satyendra K