﻿ 算子分裂有限元方法求解二维Burgers方程

# 算子分裂有限元方法求解二维Burgers方程The Operator Splitting Finite Element Method for Two-Dimensional Burgers Equation

Abstract: This paper proposes a new operator splitting finite element method for two-dimensional Burgers equation. The new method is used to decompose the Burgers equation into pure convection and diffusion part: the time discretization of the convection equation solved by the central difference scheme, and the space discretization by the standard Galerkin finite element method; the time discretization of the diffusion equation solved by the backward difference scheme, and the space discretization still using the standard Galerkin finite element method. The characteristic of this method is that the convection part is specially processed, using multi-step technology to expand the stability of the region and selecting the appropriate number of steps, the multi-step scheme can present unconditionally stable. The stability and convergence of the algorithm are verified by numerical experiments.

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