Premium
Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
Author(s) -
Lazarov Raytcho,
Repin Sergey,
Tomar Satyendra K.
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20386
Subject(s) - mathematics , approximations of π , discontinuous galerkin method , a priori and a posteriori , projection (relational algebra) , galerkin method , partial differential equation , boundary value problem , mathematical analysis , finite element method , algorithm , philosophy , physics , epistemology , thermodynamics
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