KMS Of Academy of mathematics and systems sciences, CAS
| Central discontinuous Galerkin methods on overlapping meshes for wave equations | |
| Liu, Yong1; Lu, Jianfang2; Shu, Chi-Wang3; Zhang, Mengping4 | |
| 2021-02-18 | |
| Source Publication | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
 |
| ISSN | 0764-583X |
| Volume | 55Issue:1Pages:329-356 |
| Abstract | 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. |
| Keyword | Optimal error estimates central DG method second order wave equation dispersion analysis |
| DOI | 10.1051/m2an/2020069 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | China Scholarship Council ; China Postdoctoral Science Foundation[2020TQ0343] ; NSFC[11871448] ; NSFC[11901213] ; NSF[DMS-1719410] ; NSF[DMS-2010107] ; AFOSR[FA9550-20-1-0055] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000619239500012 |
| Publisher | EDP SCIENCES S A |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58186 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Lu, Jianfang |
| Affiliation | 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 |
| Recommended Citation 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. |
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