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Pointwise a posteriori error analysis of a discontinuous Galerkin method for the elliptic obstacle problem

Ayuso De Dios, B and Gudi, T and Porwal, K (2023) Pointwise a posteriori error analysis of a discontinuous Galerkin method for the elliptic obstacle problem. In: IMA Journal of Numerical Analysis, 43 (4). pp. 2377-2412.

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Official URL: https://doi.org/10.1093/imanum/drac046


We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the conforming part of the solution obtained via a constrained averaging operator. The corrector function accounts properly for the nonconformity of the approximation and it is estimated by direct use of the Green's function of the unconstrained elliptic problem. The use of the continuous maximum principle guarantees the validity of the analysis without mesh restrictions but with shape regularity. The proposed residual-type estimators are shown to be reliable and efficient. Numerical results in two dimensions are included to verify the theory and validate the performance of the error estimator. © 2022 The Author(s). Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Item Type: Journal Article
Publication: IMA Journal of Numerical Analysis
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Error analysis; Finite element method; Galerkin methods; Variational techniques, A-posteriori error estimates; Discontinous Galerkin methods; Discontinuous galerkin; Elliptic obstacle problem; Finite element; Obstacle problems; Point wise; Posteriori error analysis; Supremum; Variational inequalities, Lagrange multipliers
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 07 Nov 2023 04:23
Last Modified: 07 Nov 2023 04:23
URI: https://eprints.iisc.ac.in/id/eprint/83059

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