Keywords : finite element scheme

Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction

Ann Jalal; Mohammed O. Al-Amr

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 3, Pages 117-128
DOI: 10.33899/csmj.2013.163531

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 .