Finite element schemes for a class of nonlocal parabolic systems with moving boundaries

TL;DR

This paper develops finite element schemes for nonlinear reaction-diffusion nonlocal systems with moving boundaries, establishing convergence, error bounds, and comparing numerical methods through tests.

Contribution

It introduces a finite element approach with coordinate transformation for nonlocal parabolic systems with moving boundaries, including convergence and error analysis.

Findings

Finite element schemes achieve convergence for the systems.

Error bounds are established for the numerical solutions.

Numerical tests compare fixed and moving finite element methods.

Abstract

The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with a moving finite element method are investigated.