Mixed Finite Element Method And Least-squares Finite Element For Nonlinear MHD Equations

In the study of the magnetic field of unsteady conductive fluid in the process, we have the equation is nonlinear, which makes the flow of magnetic fluid dynamics of complex mathematicalanalysis, but we can use numerical method. Although their solution is to simplify the situation, but clearly articulate the basic flow pattern, use these laws can at least qualitatively discussed more complex magnetic fluid flow dynamics.As is often not. practical problems in the most general form of demand equations solution, but only the needs of a particular group of the equation, the study of simplified equation. we can get the solution of practical value.In this paper, mixed finite element method and least-squares finite element method followingan idealized nonlinear equations were analyzed:-v△u + (u·▽)u +▽p-ρ(▽×B)×B = f inΩ▽·u= 0 inΩk▽×▽×B -▽×(u×B) = g inΩ▽·B = 0 inΩ(1.1)u = 0 onΓB·n = 0 onΓcurlB×n = 0 onΓThrough analysis.the existence of finite element analysis and error estimates are demonstrated.It has been divided into three chapters:ChapterⅠis prepared knowlcdge,will be given at the back to use the conclusions of the main elliptic equation is the existence of mixed finite element solution of the basic conditions.ChapterⅡis inixed finite element method, first of all.it is the definition of the basic function space, followed by steady given the nonlinear MHD equations, and derives weak form. once again mixed finite element; solution is the existence of proof .finally ,a mixed finite element analysis of the convergence of solutions is demonstrated.ChapterⅢis the least-squares finite element method, the first.is least-squares form, and then prove the existence of solutions, finally, is in the convergence of analysis.