Zurück zu den Preprints des Jahres 2005


2005-03

Partitioning methods for reaction-diffusion problems

by Heineken, W., Warnecke, G..


Series: 2005-03, Preprints

MSC:
65L06 Multistep, ~Runge-Kutta and extrapolation methods
65M50 Mesh generation and refinement
35K57 Reaction-diffusion equations
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

Abstract:
We consider the numerical solution of reaction-diffusion systems using linear finite elements on an adaptive triangular grid in space and partitioned W-methods in time. For grid adaption an algorithm featuring a flexible refinement and coarsening control is proposed. The partitioned W-methods keep the stability of implicit schemes but reduce the size of the linear systems to be solved. We combine local partitioning with partitioning between the diffusion and reaction terms, leading to a large variety of methods. The efficiency if partitioned schemes are used instead of a fully implicit W-method. We include a numerical comparison of three linear solvers. Optimal truncation of the iteration process is discussed.

Keywords:
local partitioning methods, reaction-diffusion systems, W-methods, finite element method, grid adaption