Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber

We study a semi-discrete finite element approximation of weak solutions to a moving boundary problem that models the diffusion of solvent into rubber. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants and respectively for the 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.