中文版 | English
Title

A C 0interior penalty method for m th-Laplace equation

Author
Corresponding AuthorQiu, Weifeng
Publication Years
2022-11-01
DOI
Source Title
ISSN
2822-7840
EISSN
2804-7214
Volume56Pages:2081-2103
Abstract
In this paper, we propose a C0 interior penalty method for mth-Laplace equation on bounded Lipschitz polyhedral domain in Rd, where m and d can be any positive integers. The standard H1-conforming piecewise r-th order polynomial space is used to approximate the exact solution u, where r can be any integer greater than or equal to m. Unlike the interior penalty method in Gudi and Neilan [IMA J. Numer. Anal. 31 (2011) 1734- 1753], we avoid computing Dm of numerical solution on each element and high order normal derivatives of numerical solution along mesh interfaces. Therefore our method can be easily implemented. After proving discrete Hm-norm bounded by the natural energy semi-norm associated with our method, we manage to obtain stability and optimal convergence with respect to discrete Hm-norm. The error estimate under the low regularity assumption of the exact solution is also obtained. Numerical experiments validate our theoretical estimate.
© The authors. Published by EDP Sciences, SMAI 2022.
Indexed By
EI ; SCI
Language
English
SUSTech Authorship
Others
Funding Project
The work of Huangxin Chen is supported by the NSF of China (Grant Nos. 12122115, 11771363). The work of Jingzhi Li was partially supported by the NSF of China No. 11971221, Guangdong NSF Major Fund No. 2021ZDZX1001, the Shenzhen Sci-Tech Fund Nos. RCJC20200714114556020, JCYJ20200109115422828 and JCYJ20190809150413261, and Guangdong Provincial Key Laboratory of Computational Science and Material Design No. 2019B030301001. Weifeng Qiu’s research is partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China. (Project Nos. CityU 11302219, CityU 11300621).
WOS Accession No
WOS:000878309200001
Publisher
EI Accession Number
20230113333416
EI Keywords
Constrained optimization ; Integrodifferential equations ; Laplace transforms ; Polynomials
ESI Classification Code
Algebra:921.1 ; Calculus:921.2 ; Mathematical Transformations:921.3 ; Systems Science:961
ESI Research Field
MATHEMATICS
Data Source
EV Compendex
Citation statistics
Cited Times [WOS]:0
Document TypeJournal Article
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/519785
DepartmentDepartment of Mathematics
深圳国际数学中心(杰曼诺夫数学中心)(筹)
Affiliation
1.School of Mathematical Sciences and Fujian Provincial, Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian; 361005, China
2.Department of Mathematics and National, Center for Applied Mathematics Shenzhen and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen; 518055, China
3.Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Recommended Citation
GB/T 7714
Chen, Huangxin,Li, Jingzhi,Qiu, Weifeng. A C 0interior penalty method for m th-Laplace equation[J]. ESAIM: Mathematical Modelling and Numerical Analysis,2022,56:2081-2103.
APA
Chen, Huangxin,Li, Jingzhi,&Qiu, Weifeng.(2022).A C 0interior penalty method for m th-Laplace equation.ESAIM: Mathematical Modelling and Numerical Analysis,56,2081-2103.
MLA
Chen, Huangxin,et al."A C 0interior penalty method for m th-Laplace equation".ESAIM: Mathematical Modelling and Numerical Analysis 56(2022):2081-2103.
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