  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.
