Multiscale analysis and simulation of a reaction-diffusion problem with transmission conditions
The multiscale method as a form of homogenization technique is used by the authors for finding solutions to reaction-diffusion problems with some transmission conditions. The paper is well organized and the appropriate references acknowledged. The variational formulation of the problem is stated nicely and is is shown that the sequence \((u^+_{0N}, u^-_{0N}, u_N^M)\) is bounded in the appropriate spaces, enabling them to extract subsequences which converge weakly in the chosen spaces. This enables the authors to obtain the unique weak solution and hence the convergence of the whole sequence of Galerkin approximates. They finally illustrate their results by means of numerical simulations.
scientific article; zbMATH DE number 5810876