Title | A C 0interior penalty method for m th-Laplace equation |
Author | |
Corresponding Author | Qiu, Weifeng |
Publication Years | 2022-11-01
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DOI | |
Source Title | |
ISSN | 2822-7840
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EISSN | 2804-7214
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Volume | 56Pages: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 | |
Language | English
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SUSTech Authorship | Others
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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).
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WOS Accession No | WOS:000878309200001
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Publisher | |
EI Accession Number | 20230113333416
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EI Keywords | Constrained optimization
; Integrodifferential equations
; Laplace transforms
; Polynomials
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ESI Classification Code | Algebra:921.1
; Calculus:921.2
; Mathematical Transformations:921.3
; Systems Science:961
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ESI Research Field | MATHEMATICS
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Data Source | EV Compendex
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Citation statistics |
Cited Times [WOS]:0
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Document Type | Journal Article |
Identifier | http://kc.sustech.edu.cn/handle/2SGJ60CL/519785 |
Department | Department 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.
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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.
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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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