Functional A Posteriori Error Estimates for Discontinuous Galerkin Approximations of Elliptic Problems

摘要

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.