Adaptive quadratic finite element method for the unilateral contact problem

TL;DR

This paper develops and analyzes an adaptive quadratic finite element method with a posteriori error estimates for the unilateral contact problem, demonstrating its reliability and efficiency through numerical results.

Contribution

It introduces a novel a posteriori error estimator for quadratic finite element methods applied to unilateral contact problems, with a focus on reliability and efficiency.

Findings

The error estimator is reliable and efficient.

Numerical results confirm the effectiveness of the adaptive method.

The method improves solution accuracy for contact problems.

Abstract

In this paper, we present and analyze a posteriori error estimates in the energy norm of a quadratic finite element method for the frictionless unilateral contact problem. The reliability and the efficiency of a posteriori error estimator is discussed. The suitable decomposition of the discrete space $\b{V^h}$ and a discrete space $\b{Q^h}$, where the discrete counterpart of the contact force density is defined, play crucial role in deriving a posteriori error estimates. Numerical results are presented exhibiting the reliability and the efficiency of the proposed error estimator.