Numerical Method Of Nonlocal Initial Boundary Value Problem

This paper pay main attention on the research on three different equations in conditions of nonlocal boundary value and initial value. In the introduction, it simply introduces the application and current researches of nonlocal problem and other main problems as well. In Chapter 2, it lists out some propaedeutics; Chap-ter 3 is the main part of this paper, which uses finite element method to solve three kinds of equations. The homogeneous elliptic equation is firstly discussed after constructing a new Hilbert space and a relevant finite element space, and it further leads to projection operator, and then the generalized Lax-Milgram theo-rem is established under some hypotheses. Therefore, it proves the well-posedness of the problems. Moreover, by using theory of error analysis, the optimal error es-timation of new space's interpolation function is obtained. For non-homogeneous elliptic equation, the non-homogeneous problem can be changed into homoge-neous problem by constructing a new function which satisfies some condition. For the non-source parabolic equations p(t)=0, the forms of semi-discrete and fully-discrete are given, and some relevant error estimation of finite element is also provided.In Chapter 4, it uses superposition principle to discuss the source parabolic equation and provides a concrete discretization scheme and relevant error estimation.