A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY

doi:10.1137/17M1152103

	A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY
	Gong, Wei1,2 ; Hu, Weiwei 3; Mateos, Mariano 4; Singler, John ; Zhang, Xiao 5,6; Zhang, Yangwen
	2018
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	56 期号:4 页码:2262-2287
摘要	In 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.
关键词	Dirichlet boundary control hybridizable discontinuous Galerkin method (HDG) error analysis low regularity convection diffusion
DOI	10.1137/17M1152103
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000443291900012
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31186
专题	计算数学与科学工程计算研究所
通讯作者	Gong, Wei
作者单位	1.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
推荐引用方式 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.