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

Abdeluaab Lidouh and Rachid Messaoudi

International Journal of Differential Equations, 2018, vol. 2018, 1-15

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

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:4650512

DOI: 10.1155/2018/4650512

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