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稳态对流扩散方程边值问题的一种有限元求解方法A Finite Element Method for Solving the Boundary Value Problem of the Steady Convection-Diffusion Equation
邱俊, 姚世举, 王汉权
稳态对流扩散方程, 边值问题, 有限元法, 非均匀网格, 边界层Steady Convection-Diffusion Equation, Boundary Value Problem, Finite Element Method, Nonuniform Grids, Boundary Layer
《Advances in Applied Mathematics》, Vol.5 No.1, 2016-02-29
In this article, we aim to design a finite element method for solving the boundary value problem of the steady convection-diffusion equation. This boundary value problem is different from the general one, in which there is a small term in the equation, which will make us difficult to design a higher-order numerical method for such problem. We first design two standard finite element methods (including linear and quadratic finite element method) to solve this boundary value problem; we next use these two methods to obtain the approximated solution, and compare the approximated solution with the analytical one in Matlab; we finally propose suggestions to improve these two standard finite element methods based on nonuniform grids, in order to find a better approximation to the boundary value problem of the convection-diffusion equation.