摘要
重点研究了二阶椭圆问题的一种混合变分形式,在该形式中,连续双线性型a（·,·）在H×H和H_h×H_h中自然满足强椭圆性.同时,格式绕开了散度空间H（div）,b（·,·）在H_h×M_h中能够容易满足离散的BB条件,并结合三维单纯形Hermite元以及矩形Adini元构造出三棱柱Hermite插值单元,同时证明了其适定性.最后,给出相应的剖分格式以及最优误差估计,证明了三棱柱Hermite元应用到此混合变分形式中是收敛的.
This paper focuses on the research of a new mixed variational form. In this variational form, a（.,-） satisfies strong ellipticity naturally and this form steers clear of the space of H（div）. Meanwhile, b（., .） satisfies discrete BB condition. Combining with three- dimensional simplex Hermite elements and rectangular Adini elements, this paper constructs a triangular prism Hermite elements and proves its well-posedness. At last, we give the corresponding subdivision scheme and the optimal error estimates, and prove its convergence.
作者
张宗标
王仲池
李猛
ZHANG Zong-biao;WANG Zhong-chi;LI Meng(Department of Education, Bozhou College, Bozhou 236800, China;Statistics and Applied Mathematics Department, Anhui University of Finance and Economic, Bengbu 233030, China;School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)
出处
《数学的实践与认识》
北大核心
2018年第8期258-264,共7页
Mathematics in Practice and Theory
基金
安徽省教育厅自然科学研究重点项目(KJ2016A492)
安徽省教育厅质量工程项目精品资源共享课《数学建模》(2016gxx093)
安徽省高校优秀青年人才支持计划(gxyq2017110)
毫州学院科研项目矩阵方程AX=BXD的约束解及其最佳逼近(BSKY201425)
关键词
三棱柱Hermite元
二阶椭圆问题
混合变分格式
误差估计
triangular prism
hermite elements
second-order elliptic problem
mixed variational form
error estimates
