arrow
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

Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-19-101, author = {Nepal , SurendraWondmagegne , Yosief and Muntean , Adrian}, 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:
Copy to clipboard
The citation has been copied to your clipboard