A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem

Kamana Porwal; Ritesh Singla

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arXiv · 2405.04961

A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem

Kamana Porwal·Ritesh Singla

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Abstract

In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$ polynomials, where $r=0$ and $s$ is either $0$ or $1$. The discrete obstacle constraints are specifically applied to the cell unknowns. The analysis hinges on the construction of a suitable Lagrange multiplier, a residual functional and a linear averaging map. The reliability and the efficiency of the proposed a posteriori error estimator is discussed, and the study is concluded by numerical experiments supporting the theoretical results.

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Kamana Porwal, Ritesh Singla. 2024-05-08. A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem. https://arxiv.org/abs/2405.04961

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