| Sobolev 方程的$H^1$-Galerkin混合有限元方法 |
| |
| 引用本文： | 郭玲,陈焕贞.Sobolev 方程的$H^1$-Galerkin混合有限元方法[J].系统科学与数学,2006,26(3):301-314. |
| |
| 作者姓名： | 郭玲 陈焕贞 |
| |
| 作者单位： | 山东师范大学数学系,济南,250014 |
| |
| 基金项目： | 国家自然科学基金(10271068)
山东省自然科学基金(Y2002A01)资助课题． |
| |
| 摘 要： | 对Sobolev方程采用H1-Galerkin混合有限元方法进行数值模拟．给出了一维空间中该方法的半离散和全离散格式及其最优误差估计;并将该方法推广到二维和三维空间．与H1-Galerkin有限元方法相比,该方法不仅降低了对有限元空间的连续性要求;而且与传统的混合有限元方法具有相同的收敛阶,但其有限元空间的选取却不需要满足LBB相容条件．数值例子将进一步说明该方法的可行性与有效性．
|
| 关 键 词： | H1-Galerkin混合有限元方法 Sobolev方程 最优误差估计 |
| 修稿时间： | 2004年1月13日 |
$H^1$-Galerkin Mixed Finite Element Method For The Sobolev Equation |
| |
| Guo Ling,Chen Huanzhen.$H^1$-Galerkin Mixed Finite Element Method For The Sobolev Equation[J].Journal of Systems Science and Mathematical Sciences,2006,26(3):301-314. |
| |
| Authors: | Guo Ling Chen Huanzhen |
| |
| Institution: | Department of Mathematics, Shandong Normal University, Jinan 250014 |
| |
| Abstract: | In this paper, an $H^1$-Galerkin mixed finite element method is
proposed to simulate the Sobolev equation. The problem is considered in
$n$-dimentional($n\leq 3$) space, respectively. The unique existence of the semi-discrete and a fully discrete
$H^1$-Galerkin mixed finite element solutions is proved, and optimal
error estimates are also established. In particular, our method can simultaneously
approximate the scalar unknown and the vector flux effectively, without requiring
the LBB consistency condition. Finally, numerical results are provided to illustrate
the efficiency of our method. |
| |
| Keywords: | H1-Galerkin mixed finite element method Sobolev equation optimal error estimates |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《系统科学与数学》浏览原始摘要信息 |
| 点击此处可从《系统科学与数学》下载免费的PDF全文 |
