发展基于RIESZ表示算子的最小二乘混合有限元方法

数学物理学报 ›› 2000, Vol. 20 ›› Issue (2): 169-180.

发展基于RIESZ表示算子的最小二乘混合有限元方法

(中国科学院计算数学与科学工程计算研究所北京 100080)

出版日期:2000-03-03 发布日期:2000-03-03

Least-Quares Mixed Finite Element Methods Based on Riesz-Representing Operators for Saddle-Point Problems

(Institute of Computational Mathematics and Scientific Engineering Computing, Chinese Academy of Sciences, Beijing 100080)

Online:2000-03-03 Published:2000-03-03

摘要/Abstract

摘要：

针对一类广义抽象混合结构变分方程，研究了其解的存在唯一性问题；同时发展基于Riesz表示算子的有限元方法.

关键词: 广义混合变分问题, Ｒｉｅｓｚ表示算子, Ｂａｂｕˇ ｓｋａＢｒｅｚｚｉ有限元法, 充分离散, 一致强制性, 不可压缩Ｓｔｏｋｅｓ问题．

Abstract:

The existence and uniqueness of a generalized saddle point problems dependent parameter is studied. Based on the Riesz-representing operators, a least squares mixed finite element method is developed for saddle point problems considered.

Key words: ｇｅｎｅｒａｌｉｚｅｄｓａｄｄｌｅｐｏｉｎｔｐｒｏｂｌｅｍｓ, Ｒｉｅｓｚｒｅｐｒｅｓｅｎｔｉｎｇｏｐｅｒａｔｏｒｓ, Ｂａｂｕˇ ｓｋａＢｒｅｚｚｉｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓ, ＩｎｃｏｍｐｒｅｓｓｉｂｌｅＳｔｏｋｅｓｆｌｏｗ

段火元. 发展基于RIESZ表示算子的最小二乘混合有限元方法[J]. 数学物理学报, 2000, 20(2): 169-180.

Duan Huoyuan. Least-Quares Mixed Finite Element Methods Based on Riesz-Representing Operators for Saddle-Point Problems [J]. Acta mathematica scientia,Series A, 2000, 20(2): 169-180.

参考文献

１　ＢｏｃｈｅｖＰＢ，ＧｕｎｚｂｕｒｇｅｒＭＤ．Ｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｏｆｌｅａｓｔｓｑｕａｒｅｓｔｙｐｅ．ＳＩＡＭＲｅｖ，１９９８，４０：７８９－８３７
２　ＢｒｅｚｚｉＦ，ＦｏｒｔｉｎＭ．ＭｉｘｅｄａｎｄＨｙｂｒｉｄＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｓ．ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９９１
３　ＤｅａｎｇＪＭ，ＧｕｎｚｂｕｒｇｅｒＭＤ．ＩｓｓｕｅｓｒｅｌａｔｅｄｔｏｌｅａｓｔｓｑｕａｒｅｓｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｆｏｒｔｈｅＳｔｏｋｅｓｅｑｕａｔｉｏｎｓ．ＳＩＡＭＪＳｃｉＣｏｍｐｕｔ，１９９８，２０：８７８－９０６
４　ＦｒａｎｃａＬＰ，ＨｕｇｈｅｓＴＪＲ，ＳｔｅｎｂｅｒｇＲ．Ｓｔａｂｉｌｉｚｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓ．Ｉｎ：ＩｎｃｏｍｐｒｅｓｓｉｂｌｅＣｏｍｐｕｔａｔｉｏｎａｌＦｌｕｉｄＭｅｃｈａｎｉｃｓ．ＧｕｎｚｂｕｒｇｅｒＭＤ，ＮｉｃｏｌａｉｄｅｓｅｄｓＲＡ．ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓ，１９９３．８７－１０６
５　ＺｈｏｕＴＸ．Ｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｏｎｔｈｅｃｏｍｂｉｎａｔｉｏｎｏｆｐｒｉｍｉｔｉｖｅｄｕａｌｍｏｄｅｌｓｆｏｒｓａｄｄｌｅｐｏｉｎｔｐｒｏｂｌｅｍｓ．ＳｃｉｅｎｃｅｓｉｎＣｈｉｎａＳｅｒｉｅｓＥ，１９９７，２７：７５－８７
６　Ｄｕａｎｈｕｏｙｕａｎ．Ｎｅｗｍｉｘｅｄａｎｄｈｙｂｒｉｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓ（ｉｎｃｈｉｎｅｓｅ）．ＴｈｅｓｉｓＩｎｓｔｉｔｕｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓａｎｄＳｃｉｅｎｔｉｆｉｃ／ＥｎｇｉｎｅｅｒｉｎｇＣｏｍｐｕｔｉｎｇ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｅｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ，Ｍａｙ１９９７