A G/L-S Stabilized Finite Element Method For The Stationary Dissymmetry Flow Equations

The stationary dissymmetry flow problem has very important physical dynamics background that summarized in some papers. Some papers have processed severe mathematics analysis, gained existence and uniqueness of the solution. But few papers have numerical research of the problem. The present paper deals with the numerical solution by means of Stabilized Finite Element Methods. That G/L-S finite element discrete form is used in this paper has the following reasons: (1) a G/L-S stabilized finite element method doesn't request BB condition come into existence; (2)Paper[l] is an successful application of the G/L-S method [5] to N-S equations and its altrenative [6] to nonlinear equations; (3)Compared with N-S equations, the stationary dissymmetry flow equations are more complicated which increases the difficulties of theory and numerical analysis; (4)The mix variational form is educed and existence and uniqueness of the solution are proved. A G/L-S finite element discrete form is proposed. The discrete solution is stable for any combination of finite element spaces. But also the convergence and error estimate of the finite element solution are showed.