Modeling, Analysis and Simulation: An A Posteriori Adaptive Mesh Technique for Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer

摘要

We study numerical approximation for a class of singularly perturbed problems of convection-diffusion type with a moving interior layer. In a domain (a segment) with a moving interface between two subdomains, we consider an initial boundary value problem for a singulary perturbed parabolic convection-diffusion equation. Convection fluxes on the subdomains are directed towards the interface. The solution of this problem has a moving transition layer in the neighbourhood of the interface. Unlike problems with a stationary layer, the solution exhibits singular behaviour also with respect to the time variable.