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

TL;DR

This paper develops an a posteriori error analysis for hybrid high-order methods applied to the elliptic obstacle problem, providing reliable error estimators and validating them through numerical experiments.

Contribution

It introduces a novel a posteriori error estimator for hybrid high-order methods tailored to the elliptic obstacle problem, including the construction of a Lagrange multiplier and residual functional.

Findings

The error estimator is both reliable and efficient.

Numerical experiments confirm the theoretical error bounds.

The method effectively handles obstacle constraints on cell unknowns.

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.