Convergence Analysis For Non Linear System Of Parabolic Variational Inequalities

TL;DR

This paper provides a comprehensive numerical analysis for nonlinear parabolic variational inequalities, establishing existence, convergence of solutions, and applicability across various numerical schemes.

Contribution

It offers a unified framework for analyzing convergence and existence of solutions for nonlinear parabolic PVIs with Dirichlet boundary conditions.

Findings

Proves existence of exact solutions.

Establishes convergence of approximate solutions.

Applicable to multiple numerical schemes.

Abstract

This work aims to provide a comprehensive and unified numerical analysis for non linear system of parabolic variational inequalities (PVIs) subject to Dirichlet boundary condition. This analysis enables us to establish an existence of the exact solution to the considered model and to prove the convergence for the approximate solution and its approximate gradient. Our results are applicable for several conforming and non conforming numerical schemes.