Numerical Simulation Method For Burgers Equations

This paper focuses on the numerical solutions to two partial differential equations. This paper studies implicit-explicit multistep finite element method and two splitting least squares mixed finite element method for Burgers equation, and use implicit-explicit multistep finite element method to study reaction-diffusion equations. Implicit-explicit multistep finite element method combines the implicit and explicit multistep method and finite element method, One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient. Two splitting least squares mixed finite element method discretizes the equations in time layer firstly, then introduce an unknown variable to get a coupled equations. And then decompose the domain, the coupled system can be splited into two independent sub-systems, so reduce the difficulty and scale of primal problems. Theoretical analysis shows that the method can get approximate solutions for the primal problems with optimal accuracy in ( )L2Ωnorm. This paper theoretical analysis on implicit-explicit multistep finite element method and two splitting least squares mixed finite element method, and verify the reasonableness of the two structures.The main results of this paper are outlined as follows: In chapter one, the paper briefly introduces the development process of finite element method and some basic knowledge used in the latter part of this paper.In chapter two, the paper studies implicit-explicit multistep finite element method for Burgers equation.In chapter three, the paper studies two splitting least squares mixed finite element method for Burgers equation. In chapter four, the paper studies implicit-explicit multistep finite element method for some nonlinear reaction-diffusion equations.