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A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY
Gong, Wei1,2; Hu, Weiwei3; Mateos, Mariano4; Singler, John; Zhang, Xiao5,6; Zhang, Yangwen
2018
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume56Issue:4Pages:2262-2287
AbstractIn the first part of this work, we analyzed an unconstrained Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D convex polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity, and we use a different analysis approach. We again prove an optimal convergence rate for the control and present numerical results to illustrate the convergence theory.
KeywordDirichlet boundary control hybridizable discontinuous Galerkin method (HDG) error analysis low regularity convection diffusion
DOI10.1137/17M1152103
Language英语
Funding ProjectNational Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; DIG ; FY 2018 ASR+1 Program at Oklahoma State University ; Spanish Ministerio de Economia y Competitividad[MTM2014-57531-P] ; Spanish Ministerio de Economia y Competitividad[MTM2017-83185-P] ; National Science Foundation[DMS-1217122] ; Institute for Mathematics and its Applications at the University of Minnesota
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000443291900012
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31186
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
3.Oklahoma State Univ, Dept Math, Stillwater, OK 74075 USA
4.Univ Oviedo, Dept Matemat, Campus Gijon, Gijon 33203, Asturias, Spain
5.Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA
6.Sichuan Univ, Coll Math, Chengdu 610065, Sichuan, Peoples R China
Recommended Citation
GB/T 7714
Gong, Wei,Hu, Weiwei,Mateos, Mariano,et al. A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2018,56(4):2262-2287.
APA Gong, Wei,Hu, Weiwei,Mateos, Mariano,Singler, John,Zhang, Xiao,&Zhang, Yangwen.(2018).A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY.SIAM JOURNAL ON NUMERICAL ANALYSIS,56(4),2262-2287.
MLA Gong, Wei,et al."A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY".SIAM JOURNAL ON NUMERICAL ANALYSIS 56.4(2018):2262-2287.
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