Weak Galerkin Finite Element Method For Time-fractional Nonlinear Integro-differential Equations

In recent years,the weak Galerkin finite element method has attracted wide attention in the field of numerical solutions of par-tial differential equations.More and more scholars have used this method and discovered some properties such as preserves important physical quantities of partial differential equation(such as mass or energy conservation).In this thesis,a fully discrete scheme for one-dimensional time fractional nonlinear integro-differential equation is established based on the weak Galerkin finite element method.The stability and con-vergence of this scheme are proved.Several numerical experiments are presented to illustrate the theoretical analysis and to show the strong potential of this method.The structure of this paper is as follow:In chapter 1,we in-troduce the development background of fractional order integral differential equation and the the research statue of weak Galerkin finite element method.In chapter 2,we introduce the basic con-cepts of fractional derivative and some definitions used in the re-search.In chapter 3,we present the weak Galerkin finite element method and derive the fully discrete weak Galerkin finite element scheme.In chapter 4,we use the energy method to analysis the stability and convergence of the fully discrete scheme.In chapter 5,we give some numerical example to verify our theoretical results.Finally,we have made a summary and outlook to this paper.