Error Estimates for Semi-Discrete Finite Element Approximations for a Moving Boundary Problem Capturing the Penetration of Diffusants into Rubber
Year: 2022
Author: Surendra Nepal, Yosief Wondmagegne, Adrian Muntean
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 101–125
Abstract
We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20351
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 101–125
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Moving boundary problem finite element method method of lines a priori error estimate a posteriori error estimate diffusion of chemicals into rubber.