The Numerical Methods For Two-dimensional Burgers Equation

Burgers equation is a kind of nonlinear partial differential equation with convection and diffusion terms,which maintains the mixed type of the Navier-Stokes equation and can be regarded as a simplified model of the Navier-Stokes equation.Therefore,the study of this equation has important theoretical significance and applied value.This paper mainly studies the numerical methods of nonlinear Burgers equation and corresponding error analysis.The main work is as follows:In the second chapter,according to the definition and properties of Multi-Quadric quasi-interpolation,it is applied to the initial boundary value problem of one-dimensional Burgers equation.The convergence and stability are verified by numerical experiments.In the third chapter,the finite element method for the two-dimensional Burgers equation is discussed.By using the properties of projection,the error estimates of finite element solution and the interpolation of the exact solution about L~2norm can be obtained under semi-discrete and four kinds of fully-discrete schemes.Finally,we carry out a numerical example to verify the efficiency of the method.In the fourth chapter,the mixed finite element method for the two-dimensional Burgers equation is discussed,and the semi-discrete scheme and Crank-Nicolson fully discrete scheme are given.By using the properties of projection,the error estimates of the unknown function and the gradient of the unknown function about L~2norm can be obtained.