Finite element analysis of diffusion with reaction at a moving boundary
The authors model an isothermal chemical reaction occurring at an unknown moving boundary. The one-dimensional mathematical formulation leads to two coupled differential equations, the first one being partial and the second one ordinary. A variational approach combined with suitable transformation of spatial variable gives an integral identity. The finite element approximation yields a semidiscrete system of ordinary differential equations. This one, after nondimensionalization, is integrated with help of predictor and predictor-corrector methods. Special attention is devoted to quasi-state case when diffusion is very strong in comparison to reaction. For this case, analytical solution, finite element solution and solution obtained via perturbation method are compared. The first-order and second-order reaction rate are tested numerically.
scientific article; zbMATH DE number 4115902