Finite Element Method For Nonlocal Elliptic And Parabolic Problem

In this paper,we study elliptic equation and parabolic equation with nonlocal boundary condition and initial condition, the study of nonlocal problem of a broad background has important theoretical and applied value. In the introduction part, we introduce the origin of the non-local boundary value problems,its current research state and a summary about my works in this thesis.In the second chapter, first of all, we apply the superposition principle of linear equations and the finite element superconvergence property to provide the linear finite element method for the numerical solution scheme for a class of non-local elliptic problem. Secondly, we use classical finite element analysis of the error theory to gain the finite element function and its derivative of optimal error order. Further, we will promote the conclusions of elliptic equations to non-parabolic partial initial in the numerical solution of the boundary value problems, numerical experiment results show that the numerical experiments conform to theoretical results.In the third chapter,we discuss a class of two-dimensional partial elliptic problem of finite element method with application of the basic theory of partial differential equations and the finite element analysis method the basic error. By introducing continuous reconcile orthogonal projection operator and discrete reconcile orthogonal projection operator, the error analysis is conversed to the projection operator error. With certain restrictions to the kernel function, we can obtain the results of two elliptic partial-dimensional analysis of the error.