一维非线性抛物问题两层网格有限体积元逼近

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 962-975.

一维非线性抛物问题两层网格有限体积元逼近

陈传军¹, 张晓艳¹, 赵鑫²

1. 烟台大学数学与信息科学学院山东烟台 264005;
2. 湘潭大学数学与计算科学学院湖南湘潭 411105

收稿日期:2016-06-19 修回日期:2017-01-17 出版日期:2017-10-26 发布日期:2017-10-26
作者简介:陈传军,E-mail:cjchen2001@163.com
基金资助:
国家自然科学基金（11571297）、山东省自然科学基金（ZR2014AM003）和烟台大学研究生科技创新基金

A Two-Grid Finite Volume Element Approximation for One-Dimensional Nonlinear Parabolic Equations

Chen Chuanjun¹, Zhang Xiaoyan¹, Zhao Xin²

1. School of Mathematics and Information Sciences, Yantai University, Shandong Yantai 264005;
2. School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105

Received:2016-06-19 Revised:2017-01-17 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by NSFC (11571297), Shandong Province Natural Science Foundation (ZR2014AM003) and Graduate Innovation Foundation of Yantai University

摘要/Abstract

摘要： 该文主要研究一维非线性抛物问题两层网格有限体积元逼近.对一维非线性抛物问题有限体积元解的存在性进行了讨论，给出了最优阶L²-模和H¹-模误差估计结果，并研究了其两层网格算法.证明了当粗细网格步长满足h=O（H²）时两层网格算法具有最优阶H¹-模误差估计.数值算例验证了理论结果.

关键词: 有限体积元, 两层网格, 非线性, 抛物方程, 误差估计

Abstract: In this paper, a two-grid finite volume element approximation for one-dimensional nonlinear parabolic equations is derived and studied. We develop a finite volume element approximation for one-dimensional nonlinear parabolic equations and study its existence and error analysis. Optimal error estimates in the L²-norm and H¹-norm are proved. We study the two-grid method based on the finite volume element method and optimal error estimate in the H¹-norm is proved. It is shown that we can achieve asymptotically optimal approximation when the size of grids satisfies h=O(H²). Numerical examples are presented to verify the theoretical results.

Key words: Finite volume element method, Two-grid, Nonlinear, Parabolic equation, Error estimate

中图分类号:

O241.82

陈传军, 张晓艳, 赵鑫. 一维非线性抛物问题两层网格有限体积元逼近[J]. 数学物理学报, 2017, 37(5): 962-975.

Chen Chuanjun, Zhang Xiaoyan, Zhao Xin. A Two-Grid Finite Volume Element Approximation for One-Dimensional Nonlinear Parabolic Equations[J]. Acta mathematica scientia,Series A, 2017, 37(5): 962-975.

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