# 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

DOI: 10.12677/AAM.2016.51018, PDF, HTML, XML, 下载: 1,609  浏览: 3,703  国家自然科学基金支持

Abstract: 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.

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