A stabilised finite element method for the plate obstacle problem

TL;DR

This paper presents a stabilised finite element method for the Kirchhoff plate obstacle problem, providing error estimates and numerical validation for both elastic and rigid obstacles.

Contribution

It introduces a Nitsche-type scheme with a priori and residual-based a posteriori error estimates for the plate obstacle problem.

Findings

Effective error control demonstrated through numerical experiments.

Method applicable to both elastic and rigid obstacles.

Provides theoretical and practical validation of the stabilised scheme.

Abstract

We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming $C^1$-continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.