分数阶对流扩散方程的特征有限元方法

计算物理 ›› 2017, Vol. 34 ›› Issue (4): 417-424.

分数阶对流扩散方程的特征有限元方法

朱晓钢, 聂玉峰, 王俊刚, 袁占斌

西北工业大学应用数学系, 陕西西安 710129

收稿日期:2016-06-23 修回日期:2016-09-12 出版日期:2017-07-25 发布日期:2017-07-25
作者简介:朱晓钢(1987-),男,湖南邵阳,博士生,主要从事偏微分方程的数值研究,E-mail:zhuxg590@yeah.net
基金资助:
国家自然科学基金（11471262，11501450）资助项目

A Characteristic Finite Element Method for Fractional Convection-Diffusion Equations

ZHU Xiaogang, NIE Yufeng, WANG Jungang, YUAN Zhanbin

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2016-06-23 Revised:2016-09-12 Online:2017-07-25 Published:2017-07-25

摘要/Abstract

摘要： 讨论非线性分数阶对流扩散方程的特征有限元方法.利用特征线法和分数阶有限元框架，构建一种基于特征方向的全离散有限元格式.模拟物理问题，并在数值上与常规有限元格式进行比较，计算结果表明：该方法能准确地捕捉到控制方程的精确解，即使是在对流效应占优时，也具有稳定性好和逼近精度高等特征.

关键词: 分数阶微积分, 对流扩散方程, 特征有限元方法

Abstract: A characteristic finite element method (FEM) is proposed for nonlinear fractional convection-diffusion equations. With the characteristic technique and fractional FEM framework, a fully discrete characteristic finite element scheme is constructed. It is utilized to simulate physical systems and studied in contrast with conventional schemes. It is demonstrated that the method captures exact solutions of governing equations well. The method enjoys good stability and high accuracy even if convection dominates diffusion essentially.

Key words: fractional calculus, convection-diffusion equation, characteristic FEM

中图分类号:

O241.8

朱晓钢, 聂玉峰, 王俊刚, 袁占斌. 分数阶对流扩散方程的特征有限元方法[J]. 计算物理, 2017, 34(4): 417-424.

ZHU Xiaogang, NIE Yufeng, WANG Jungang, YUAN Zhanbin. A Characteristic Finite Element Method for Fractional Convection-Diffusion Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(4): 417-424.

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