Development Stokes Equations Change Five Parameters $ Precision Of The Grid Anisotropy Analysis And The Poisson Equation

In this dissertation ,the main contents axe the anisotropic nonconfonning finite element methods with moving grid for nonstationary Stokes problem and the high accuracy analysis of nonconfonning finite element methods for Poisson equations.For nonstationary Stokes problem ,materials'anisotropic character should be considered in a boundary layer or near the angular of the domain fJ.At this time ,the subdivision to region Q is not of regularity or quasi-uniform and should be anisotropic grid ,which can describle the facts exactly.Crouzeix-Raviart element and rotary Q4 element are failed in anisotropic grid and many others either can't satisfy the anisotropic property or can't be used to the moving grid finite element method .It's proved that five nodals element presented by Professor Houde Han can overcome this shortcoming . In the third chapter ,by using the five nodals element's special property and combining the moving grid techniques,nonstationary Stokes problem are studied . At the same time ,by using the Stokes projection, the error estimates of L2- norm and energy norm of the five nodals anisotropic element approximate shceme are given.In the fourth chapter ,for the Poisson equations with Dirichlet boundary value problem, by using the special property of the five parameters nonconfonning rectagular element and new error estimate skills ,the superclose and the global superconvergence of it are presented directly, the methods proposed here are much easier than those of Wilson nonconfonning element.