A new Discrete Analysis Of Fourth Order Elliptic Variational Inequalities

TL;DR

This paper introduces the gradient discretisation method (GDM) for fourth order elliptic variational inequalities, providing a unified convergence analysis and error estimates applicable to various numerical schemes.

Contribution

It offers a new formulation of error estimates and proves unconditional convergence for all schemes within the GDM framework.

Findings

Unconditional convergence of GDM for fourth order problems

Error estimates applicable to multiple numerical schemes

Classical data assumptions suffice for convergence

Abstract

This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete convergence analysis of several numerical methods. We show that the convergence is unconditional. Classical assumptions on data are only sufficient to establish the convergence results. These results are applicable for all schemes fall in the framework of GDM.