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| Sobolev方程的连续时空有限元方法 | |
| 引用本文： | 赵智慧,李宏,罗振东.Sobolev方程的连续时空有限元方法[J].计算数学,2016,38(4):341-353. |
| 作者姓名： | 赵智慧 李宏 罗振东 |
| 作者单位： | 1. 内蒙古大学数学科学学院, 呼和浩特 010021; 2. 华北电力大学数理学院, 北京 102206 |
| 基金项目： | 国家自然科学基金(11361035;内蒙古自然科学基金(2014BS0101);内蒙古高等学校科学研究项目(NJZY14013) |
| 摘 要： | 本文研究Sobolev方程的连续时空有限元方法.首先建立Sobolev方程的连续时空有限元格式,然后证明了解的存在唯一性和稳定性并给出连续时空有限元解各种范数下的误差估计.最后给出数值算例来验证理论分析的正确性,并进一步说明本文所建立的格式关于时间可以得到比传统有限元方法更高的精度. |
| 关 键 词： | 连续时空有限元方法 Sobolev方程 误差估计 数值算例 |
| 收稿时间： | 2015-05-21; |
A SPACE-TIME CONTINUOUS FINITE ELEMENT METHOD FOR SOBOLEV EQUATION |
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| Zhao Zhihui,Li Hong,Luo Zhendong.A SPACE-TIME CONTINUOUS FINITE ELEMENT METHOD FOR SOBOLEV EQUATION[J].Mathematica Numerica Sinica,2016,38(4):341-353. | |
| Authors: | Zhao Zhihui Li Hong Luo Zhendong |
| Institution: | 1. School of Mathematical sciences, Inner Mongolia University, Hohhot 010021, China; 2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China |
| Abstract: | In this paper we study the continuous space-time finite element method for Sobolev equation, the continuous space-time formulation is given firstly. And then, we prove the existence, the uniqueness, and the stability of the continuous space-time finite element solution and give the error estimates of various norms of the continuous space-time finite element solution. Finally, we provide a numerical example to verify that correctness of theoretical analysis and to illustrate that the scheme established in this paper can obtain higher accuracy with respect to time than classical FE methods. |
| Keywords: | continuous space-time finite element method Sobolev equation error estimate numerical example |
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