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- Title
Pointwise a posteriori error analysis of a discontinuous Galerkin method for the elliptic obstacle problem.
- Authors
Dios, Blanca Ayuso de; Gudi, Thirupathi; Porwal, Kamana
- Abstract
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.
- Subjects
GALERKIN methods; A posteriori error analysis; GREEN'S functions; ELLIPTIC functions; CONFORMITY; PERFORMANCE theory
- Publication
IMA Journal of Numerical Analysis, 2023, Vol 43, Issue 4, p2377
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drac046