Weak Galerkin Finite Element Method For The Evolution Equation With Weakly Singular Kernel

The evolution equation often occurs in application such as heat conduction in material with memory,nuclear reactor,dynamics,etc.There are many scholars at home and abroad have done lots of research for numerical methods of the evolution equation.This thesis deals with the weak Galerkin finite element method for the evolution equation with a weakly singular kernel.We use the weak Galerkin finite element method to discretize the space vari-able and the backward Euler method is used for time discretization,the corresponding integral terms are discretised by the piecewise constant function,then we get a fully discrete weak Galerkin finite element scheme.The stability and convergence of the fully discrete scheme have been rigorously proved.Finally,we present some nu-merical experiments and the results of numerical experiments to verify our theoretical analysis.The whole paper is organized as follows:In chapter 1,we in-troduce the historic background of evolution equations.In chapter 2,we present the definitions of fractional derivative and the relative knowledge of weak Galerkin finite element method.In chapter 3,we use the backward Euler method and the weak Galerkin finite el-ement method for time variables and space variables,respectively,then the fully discrete weak Galerkin finite element scheme are de-rived.In chapter 4,we analyze the stability and convergence of the fully discrete scheme.Then in chapter 5,we give some numerical examples and the results of numerical experiments which support our theoretical results.In chapter 6,we give the summary and prospect of this paper.