Keywords : Galerkin method


Stability Analysis in Thin Liquid Film (Immobile Soap Film)

Rotina Jasim Al-Etewi; Zena Talal Al-Nuamy

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 13-21
DOI: 10.33899/csmj.2011.163648

This research is dedicated for analyzing the stability of a system of flow equations for soap film that has opposed for disturbance, and this analysis was done by using Galerkin method which enable to find disturbance growth from its nonexistence after making the system linearization. It was shown through the results of analysis that these equations were in stable state when the real part of wave velocity (a)  is a negative quantity, and it is  unstable state when the real part of this velocity is a positive quantity, i.e. a < 0 we get stability and this happens when the distance (do) and the source (uo) in two similar signs and when a > 0 we get unstable state and this happens when do , uo  have two different  signs.
 

A kind of Upwind Finite Element Approximations for Compressible Flow of Contamination from Nuclear Waste in Porous Media

Abbas Y. Al-Bayati; Saad A. Manaa; Ekhlass S. Al-Rawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 19-37
DOI: 10.33899/csmj.2008.163968

A non-linear parabolic system is derived to describe compressible nuclear waste disposal contamination in porous media . Galerkin method is applied for the pressure equation . For the concentration of the brine of the fluid, a kind of partial upwind finite element scheme is constructed. A numerical application is included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach.
 

Numerical Solution of Non-Linear Prey-Predator System using Finite Elements Method

Saad A. Manaa; Ahmed F. Qasem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 2, Pages 113-133
DOI: 10.33899/csmj.2007.164020

A non-linear prey-predator system solved numerically by Galerkin method, and we compare these results with the results of Pius Peter Nyaanga[6] who used finite difference methods, we found that Galerkin finite elements method is faster than finite difference method to reach equilibrium state where the density for the prey  and the predator  are equals for all the values for and , also we found that Galerkin method converges towards the steady state solutions faster than finite difference method with less steps in time.
 

On Upwind Galerkin Finite Element Method for Incompressible Flow of Contamination, from Nuclear Waste, in Porous Media

Abbas Y. Al-Bayati; Saad A. Manaa; Ekhlass S. Al-Rawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 2, Pages 107-126
DOI: 10.33899/csmj.2004.164114

Anon-linear parabolic system is derived to describe incompressible nuclear waste disposal contamination in porous media. Galerkin method is applied for the pressure equation. For the concentration, a kind of partial upwind finite element scheme is constructed. The finite element solution satisfies discrete maximum principle and converges to the solution in norm .