Error estimates for fully discrete approximation to a free boundary problem in polymer technology

Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants

“…However, much less seems to be known what concerns the analysis of fully discrete approximation schemes even for one dimensional formulations where the moving interface is in fact only a moving point (with a priori unknown location). The references [4,5] were particularly useful for our investigation. In [5] H. Y. Lee develops a fully discrete scheme for a Stefan problem with non-linear free boundary condition and investigates the order of conver-gence of the scheme.…”

“…In [5] H. Y. Lee develops a fully discrete scheme for a Stefan problem with non-linear free boundary condition and investigates the order of conver-gence of the scheme. In [4] , the authors construct and analyze fully discrete methods for a free boundary problem arising in the polymer technology. By using the Galerkin finite element formulation in space and a backward Euler scheme in time, the authors were able to prove the a priori error estimate for the concentration of the solvent and for the position of moving boundary.…”

Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants

“…However, much less seems to be known what concerns the analysis of fully discrete approximation schemes even for one dimensional formulations where the moving interface is in fact only a moving point (with a priori unknown location). The references [2,19] were particularly useful for our investigation. In [19] H. Y. Lee develops a fully discrete scheme for a Stefan problem with non-linear free boundary condition and investigates the order of convergence of the scheme.…”

“…In ref. [2], the authors construct and analyze fully discrete methods for a free boundary problem arising in the polymer technology. By using the Galerkin finite element formulation in space and a backward Euler scheme in time, the authors were able to prove the a priori error estimate for the concentration of the solvent and for the position of moving boundary.…”

“…By using the Galerkin finite element formulation in space and a backward Euler scheme in time, the authors were able to prove the a priori error estimate for the concentration of the solvent and for the position of moving boundary. At the technical level, we were very much inspired by the technique that has been used in [2] to get the a priori error bound. It is also worth mentioning that the main difference between the problem considered in these papers and our problem lies in the choice of the boundary conditions.…”