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Efficient discretization and preconditioning of the singularly perturbed Reaction Diffusion problem (2104.11337v1)
Published 22 Apr 2021 in math.NA and cs.NA
Abstract: We consider the reaction diffusion problem and present efficient ways to discretize and precondition in the singular perturbed case when the reaction term dominates the equation. Using the concepts of optimal test norm and saddle point reformulation, we provide efficient discretization processes for uniform and non-uniform meshes. We present a preconditioning strategy that works for a large range of the perturbation parameter. Numerical examples to illustrate the efficiency of the method are included for a problem on the unit square.
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