Central discontinuous Galerkin methods on overlapping meshes for wave equations

doi:10.1051/m2an/2020069

CSpace

	Central discontinuous Galerkin methods on overlapping meshes for wave equations
	Liu, Yong 1; Lu, Jianfang 2; Shu, Chi-Wang 3; Zhang, Mengping 4
	2021-02-18
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	55 期号:1 页码:329-356
摘要	In this paper, we study the central discontinuous Galerkin (DG) method on overlapping meshes for second order wave equations. We consider the first order hyperbolic system, which is equivalent to the second order scalar equation, and construct the corresponding central DG scheme. We then provide the stability analysis and the optimal error estimates for the proposed central DG scheme for one- and multi-dimensional cases with piecewise P-k elements. The optimal error estimates are valid for uniform Cartesian meshes and polynomials of arbitrary degree k >= 0. In particular, we adopt the techniques in Liu et al. (SIAM J. Numer. Anal. 56 (2018) 520-541; ESAIM: M2AN 54 (2020) 705-726) and obtain the local projection that is crucial in deriving the optimal order of convergence. The construction of the projection here is more challenging since the unknowns are highly coupled in the proposed scheme. Dispersion analysis is performed on the proposed scheme for one dimensional problems, indicating that the numerical solution with P-1 elements reaches its minimum with a suitable parameter in the dissipation term. Several numerical examples including accuracy tests and long time simulation are presented to validate the theoretical results.
关键词	Optimal error estimates central DG method second order wave equation dispersion analysis
DOI	10.1051/m2an/2020069
收录类别	SCI
语种	英语
资助项目	China Scholarship Council ; China Postdoctoral Science Foundation[2020TQ0343] ; NSFC[11871448] ; NSFC[11901213] ; NSF[DMS-1719410] ; NSF[DMS-2010107] ; AFOSR[FA9550-20-1-0055]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000619239500012
出版者	EDP SCIENCES S A
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58186
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Jianfang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R China 2.South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China 3.Brown Univ, Div Appl Math, Providence, RI 02912 USA 4.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
推荐引用方式 GB/T 7714	Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,et al. Central discontinuous Galerkin methods on overlapping meshes for wave equations[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2021,55(1):329-356.
APA	Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,&Zhang, Mengping.(2021).Central discontinuous Galerkin methods on overlapping meshes for wave equations.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,55(1),329-356.
MLA	Liu, Yong,et al."Central discontinuous Galerkin methods on overlapping meshes for wave equations".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 55.1(2021):329-356.