05-03
Partitioning methods for reaction-diffusion problems
Preprint series: 05-03, 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
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