Numerical Solution of Reaction-Diffusion Equations

Abstract

Adaptive computations of nonlinear systems of reaction-diffusion equations play an increasingly important role in dynamical process simulation. The efficient adaptation of the spatial and temporal discretization is often the only way to get relevant solutions of the underlying mathematical models. The corresponding methods are essentially based on a posteriori estimates of the discretization errors. Once these errors have been computed, we are able to control time and space grids with respect to required tolerances and necessary computational work. Furthermore, the permanent assessment of the solution process allows us to clearly distinguish between numerical and modelling errors — a fact which becomes more and more important.