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.