Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants

TL;DR

This paper introduces a fully discrete numerical scheme combining finite element and backward Euler methods to simulate diffusant penetration in rubber with a moving boundary, providing error estimates and numerical validation.

Contribution

The paper develops a novel fully discrete scheme for a moving-boundary diffusion problem in rubber, including error analysis and numerical verification of convergence.

Findings

The scheme achieves the theoretical order of convergence.

Numerical results confirm the accuracy of the error estimates.

The method effectively handles the moving boundary in the diffusion process.

Abstract

We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with the backward Euler method for the time discretization. Besides dealing with the existence and uniqueness of solution to the fully discrete problem, we derive a \textit{a priori} error estimate for the mass concentration of the diffusants, and respectively, for the position of the moving boundary. Numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.