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Keywords

finite element scheme
reaction-diffusion system
consistent scheme
lumped scheme

Abstract

In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction.  Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions  and  when . Also, the lumped scheme is stable under the conditions  and  when .    
https://doi.org/10.33899/csmj.2013.163531
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