| This paper will discuss the Stokes preblem based on the Mixed ?nite element of Q2- Q0 under the rectangle Grid. There has been some results about the ideas,the order convergence of velocity ?led is h2,the order convergence of pressure ?led is h. For the velocity ?eld, this paper adopts ‘ ‘ point- line- face ”interpolation.Using integral identities technology,prove that the pressure ?eld of the interpolation approximation is h2,and has the whole supercloseness( h2).Then we utilize the interpolation postprocessing, obtained the whole superconvergence, the order of convergence achieves to h2.This paper discusses the equation for the steady Stokes problems. In the case of small Reynolds number Re, which re?ects the steady ?ow of incompressible viscous ?uid,Solving the steady Stokes problems to deal with the full Navier- Stokes equations lays a solid foundation, so the research on its numerical solution is very meaningful. Stokes problem is a mixture of standard ?nite element method,speed and pressure calculation, at the same time is a coupling process, and the divergence is zero on speed This makes it a saddle point problem.Compared with the ?nite di?erence method, ?nite element method has good stability and better error estimation, using irregular grids, classi?cation and advantages. In order to guarantee the uniqueness of solution of Stokes problem, the solution space is not arbitrary, LBB condition to be ful?lled;Discrete equations also need to satisfy the discrete inf- sup conditions. At the same time, Stokes problems can also be regarded as a minimization problem with constraints.In chapter one, we ?rst present introduction and recent research for results on Stokes preblem; and introduce prelimilary knowledge.In chapter two, the introduction of integral identities techniques,and we utilize the techniques to proof the closeness of the Q2- Q0,Post-processing technology helps improve the order of convergence.In chapter three, we focus on Numerical Experiments. |
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