Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction
A. Al-Sawoor, and M. Al-Amr. Al-Rafidain Journal of Computer Sciences and Mathematics, 10 (3):
117-128(September 2013)
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 .
%0 Journal Article
%1 alsawoor2013fourier
%A Al-Sawoor, Ann J.
%A Al-Amr, Mohammed O.
%D 2013
%J Al-Rafidain Journal of Computer Sciences and Mathematics
%K consistent element finite lumped reaction-diffusion scheme system
%N 3
%P 117-128
%T Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction
%U http://www.iasj.net/iasj?func=fulltext&aId=79867
%V 10
%X 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 .
@article{alsawoor2013fourier,
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 .},
added-at = {2014-03-06T14:14:44.000+0100},
author = {Al-Sawoor, Ann J. and Al-Amr, Mohammed O.},
biburl = {https://www.bibsonomy.org/bibtex/216e238d136415762818b08c668f0c45b/mohammedalamr},
interhash = {45b1a00184f3777bc9ec551fd1b88efb},
intrahash = {16e238d136415762818b08c668f0c45b},
journal = {Al-Rafidain Journal of Computer Sciences and Mathematics},
keywords = {consistent element finite lumped reaction-diffusion scheme system},
month = sep,
number = 3,
pages = {117-128},
timestamp = {2014-03-06T14:14:44.000+0100},
title = {Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction},
url = {http://www.iasj.net/iasj?func=fulltext&aId=79867},
volume = 10,
year = 2013
}