A General Error Estimate For Parabolic Variational Inequalities

TL;DR

This paper develops a general error estimate for numerical solutions of parabolic obstacle problems using the gradient discretisation method, unifying convergence analysis across various numerical schemes.

Contribution

It introduces the first comprehensive error estimate for parabolic variational inequalities within the GDM framework, covering multiple numerical methods.

Findings

Convergence rates are established for various numerical schemes.

Numerical experiments confirm theoretical error estimates.

The GDM provides a unified approach for analyzing parabolic obstacle problems.

Abstract

The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the GDM to establish a first general error estimate for numerical approximations of parabolic obstacle problems. This gives the convergence rates of several well--known conforming and non conforming numerical methods. Numerical experiments based on the hybrid finite volume method are provided to verify the theoretical results.