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International Journal of Differential Equations
Volume 2018, Article ID 4650512, 15 pages
https://doi.org/10.1155/2018/4650512
Research Article

Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in

Department of Mathematics and Computer Science, Laboratory LACSA, Faculty of Sciences, Mohammed 1st University, BV Mohammed VI, P.O. Box 717, 60000 Oujda, Morocco

Correspondence should be addressed to Rachid Messaoudi; rf.oohay@sne_dihcar_m

Received 4 February 2018; Accepted 21 May 2018; Published 2 July 2018

Academic Editor: Patricia J. Y. Wong

Copyright © 2018 Abdeluaab Lidouh and Rachid Messaoudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the standard affine discontinuous Galerkin method approximation of the second-order linear elliptic equation in divergence form with coefficients in and the right-hand side belongs to ; we extend the results where the case of linear finite elements approximation is considered. We prove that the unique solution of the discrete problem converges in for every with ( or ) to the unique renormalized solution of the problem. Statements and proofs remain valid in our case, which permits obtaining a weaker result when the right-hand side is a bounded Radon measure and, when the coefficients are smooth, an error estimate in when the right-hand side belongs to verifying for every , for some