The Galerkin Space-Time Discontinuous Finite Element Method For Two Kinds Of Convection-dominated Problems

Recently,researches about discontinuous finite element methods are very hot.In this paper, we will use the Galerkin Space-Time Discontinuous Finite Element Method to process Convection-dominated Parabolic Integro-differential Equations and use the DG fractional step scheme to solve the nonlinear convection—dominated diffusion problems,and obtain the optimal estimate.In the first chapter,we mainly introduce the status of recent research of the discontinuous finite element methods and the Galerkin Space-Time Discontinuous Finite Element Method.In the second chapter,we introduce some kinds of discontinuous finite element methods and some note we will use in this paper.In the third chapter, we will use the Galerkin Space-Time Discontinuous Finite Element Method to process Convection-dominated Parabolic Integro-differential Equations,and use the union skill of Finite Element Method and Finite-difference method,in the separate sector,use the Characteristic of Lagrange Interpolation Multinomial in Radau spot ,Remove the Limiting condition of Space-Time grid in the Space-Time Discontinuous Finite Element Method,and obtaining the max mold of time and the space L2mold.In the fourth chapter,we build the DG fractional step scheme format of the nonlinear convection—dominated diffusion problems, and give the theoretical analysis. The theoretical analysis shows that the accuracy is really improved although more work is demanded.