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Volume 19, Issue 1
Error Estimates for Semi-Discrete Finite Element Approximations for a Moving Boundary Problem Capturing the Penetration of Diffusants into Rubber

Surendra Nepal, Yosief Wondmagegne & Adrian Muntean

Int. J. Numer. Anal. Mod., 19 (2022), pp. 101-125.

Published online: 2022-03

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  • 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.

  • Keywords

Moving boundary problem, finite element method, method of lines, a priori error estimate, a posteriori error estimate, diffusion of chemicals into rubber.

  • AMS Subject Headings

65M15, 65M20, 65M60, 35R37

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-101, author = {Surendra and Nepal and and 22696 and and Surendra Nepal and Yosief and Wondmagegne and and 22697 and and Yosief Wondmagegne and Adrian and Muntean and and 22698 and and Adrian Muntean}, title = {Error Estimates for Semi-Discrete Finite Element Approximations for a Moving Boundary Problem Capturing the Penetration of Diffusants into Rubber}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20351.html} }
TY - JOUR T1 - Error Estimates for Semi-Discrete Finite Element Approximations for a Moving Boundary Problem Capturing the Penetration of Diffusants into Rubber AU - Nepal , Surendra AU - Wondmagegne , Yosief AU - Muntean , Adrian JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 101 EP - 125 PY - 2022 DA - 2022/03 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20351.html KW - Moving boundary problem, finite element method, method of lines, a priori error estimate, a posteriori error estimate, diffusion of chemicals into rubber. AB -

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.

Surendra Nepal, Yosief Wondmagegne & Adrian Muntean. (2022). Error Estimates for Semi-Discrete Finite Element Approximations for a Moving Boundary Problem Capturing the Penetration of Diffusants into Rubber. International Journal of Numerical Analysis and Modeling. 19 (1). 101-125. doi:
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