一种非标准的混合有限元法求解一维退化非线性抛物问题

吉林大学学报(理学版)

一种非标准的混合有限元法求解一维退化非线性抛物问题

陈国芳¹, 吴丹², 吕俊良²

1. 吉林省教育学院, 长春 130022; 2. 吉林大学数学学院, 长春 130012

收稿日期:2017-03-20 出版日期:2017-11-26 发布日期:2017-11-29
通讯作者: 吕俊良 E-mail:lvjl@jlu.edu.cn

A Nonstandard Mixed Finite Element Method for SolvingOneDimensional Degenerate Nonlinear Parabolic Problem

CHEN Guofang¹, WU Dan², LV Junliang²

1. Jilin Provincial Institute of Education, Changchun 130022, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2017-03-20 Online:2017-11-26 Published:2017-11-29
Contact: LV Junliang E-mail:lvjl@jlu.edu.cn

摘要/Abstract

摘要： 针对用标准混合有限元法求解一维退化非线性抛物问题时, 会出现数值解波阵面不能向前传播的现象, 通过分析标准混合有限元法求解退化方程时的缺陷, 提出一种非标准的混合有限元求解方法, 该方法中间变量定义中不再包含扩散系数, 而仅为原始未知函数对空间变量的导数. 基于典型的模型问题, 在数值实验上验证了该方法的有效性.

关键词: 混合有限元法, 退化非线性抛物问题, 非线性迭代, Barenblatt解

Abstract: The numerical solution of wave front did not propagate forward when one tried to solve the onedimensional degenerate nonlinear parabolic (DNP) problem with the standard mixed finite element method. By analyzing the defect of the standard mixed finite element method for solving the degenerate equations, we proposed a nonstandard mixed finite element method. The definition of intermediate variable in the method did not include diffusion coefficient, but only the derivative of primal unknown function with respect to spatial variable. Based on typical model problems, the effectiveness of the proposed method was verified by the numerical experiments.

Key words: degenerate nonlinear parabolic problem, Barenblatt solution, nonlinear iteration, mixed finite element method

中图分类号:

O241.82

陈国芳, 吴丹, 吕俊良. 一种非标准的混合有限元法求解一维退化非线性抛物问题[J]. 吉林大学学报(理学版), 2017, 55(06): 1352-1358.

CHEN Guofang, WU Dan, LV Junliang. A Nonstandard Mixed Finite Element Method for SolvingOneDimensional Degenerate Nonlinear Parabolic Problem[J]. Journal of Jilin University Science Edition, 2017, 55(06): 1352-1358.