• 论文 •

### Sobolev方程的连续时空有限元方法

1. 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
• 收稿日期:2015-05-21 出版日期:2016-12-15 发布日期:2016-10-13
• 通讯作者: 李宏,E-mail:malhong@imu.edu.cn.研究方向:有限元方法及其应用.
• 基金资助:

国家自然科学基金（11361035，11271127，11301258），内蒙古自然科学基金（2014BS0101），内蒙古高等学校科学研究项目（NJZY14013）.

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.

### A SPACE-TIME CONTINUOUS FINITE ELEMENT METHOD FOR SOBOLEV EQUATION

Zhao Zhihui1, Li Hong1, Luo Zhendong2

1. 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
• Received:2015-05-21 Online:2016-12-15 Published:2016-10-13

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.

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