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We consider a moving boundary problem with kinetic condition that describesthe diffusion of solvent into rubber and study semi-discrete finite elementapproximations of the corresponding weak solutions. We report on both a prioriand a posteriori error estimates for the mass concentration of the diffusants,and respectively, for the a priori unknown position of the moving boundary. Ourworking techniques include integral and energy-based estimates for a nonlinearparabolic problem posed in a transformed fixed domain combined with a suitableuse of the interpolation-trace inequality to handle the interface terms.Numerical illustrations of our FEM approximations are within the experimentalrange and show good agreement with our theoretical investigation. This work isa preliminary investigation necessary before extending the current movingboundary modeling to account explicitly for the mechanics of hyperelastic rodsto capture a directional swelling of the underlying elastomer.

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