Research On Isoparametric Finite Element Method For Boundary Value Problems Of Differential Equations

Isoparametric finite element method to solve three kinds of Partial differential equations on curved domain are discussed in this paper.Firstly,an isoparametric mixed finite element method is proposed and analyzed for solving a class of fourth-order elliptic equation with Navier boundary condition.The existence and uniqueness of the numerical solution of the discrete problem are proved with the help of numerical quadrature,and the optimal error estimation with H1 norm is obtained in Qh.Secondly,an isoparametric finite element method for plane elastic problem is given without considering the Locking phenomenon.The existence and uniqueness of discrete solution are proved.The optimal H1 error estimation is also obtained in ?h,which yields better accuracy than using a convex polygonal domain to approximate the curved domain.Thirdly,a new error estimate method is used to analyze Sobolev equation,which is different from the analysis process of the previous two problems,and the corresponding convergence analysis is given.In addition,a class of curved triangle meshes are constructed,some numerical examples are tested for each problem to verify the validity of the theoretical analysis.