| 抛物型界面问题的变网格有限元方法 |
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| 引用本文： | 关宏波,洪亚鹏.抛物型界面问题的变网格有限元方法[J].计算数学,2020,42(2):196-206. |
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| 作者姓名： | 关宏波 洪亚鹏 |
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| 作者单位： | 郑州轻工业大学 数学与信息科学学院, 郑州 450002 |
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| 基金项目： | 国家自然科学基金;研究生科技创新项目;青年骨干教师基金;博士基金 |
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| 摘 要： | 本文针对抛物型界面问题，提出了一种线性三角形变网格有限元方法.其主要思路是针对空间变量采用有限元离散，对时间变量采用差分离散，但是不同时刻的有限元剖分网格可以不同.在不引入Ritz投影这一传统分析工具的情况下，得到了最优误差估计结果，使得证明过程更加简洁.给出的数值算例验证了理论分析的正确性.
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| 关 键 词： | 界面问题 线性三角形有限元 变网格 最优误差估计 |
| 收稿时间： | 2018-07-04 |
FINITE ELEMENT METHODS WITH MOVING GRIDS FOR PARABOLIC INTERFACE PROBLEMS |
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| Guan Hongbo,Hong Yapeng.FINITE ELEMENT METHODS WITH MOVING GRIDS FOR PARABOLIC INTERFACE PROBLEMS[J].Mathematica Numerica Sinica,2020,42(2):196-206. |
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| Authors: | Guan Hongbo Hong Yapeng |
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| Institution: | College of Mathematics and Information Science, Zhengzhou University of Light Industry Zhengzhou 450002, China |
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| Abstract: | In this paper, the linear triangular finite element methods with moving grids are discussed for the parabolic interface problems. The general idea is applying finite element method in space and choosing difference method with respect to the time variable, respectively, but the grids can be different when the time varies. The optimal order error estimates are obtained without introducing the Ritz projection, which is thought to be a conventional analysis tool. Thus, the analysis procedure is made to be more concise. Numerical examples are provided to verify the theoretical analysis. |
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| Keywords: | Parabolic interface problems linear triangular finite elements moving grids optimal order error estimate |
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