@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} }