Proceedings Mathematical Sciences | |
â„Ž-ð‘ Spectral element methods for three dimensional elliptic problems on non-smooth domains, Part-II: Proof of stability theorem | |
Akhlaq Husain3  P Dutt1  C S Upadhyay2  A S Vasudeva Murthy4  | |
[1] Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur 0 0, India$$;Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 0 0, India$$;Department of Mathematics, The LNM Institute of Information Technology, Jaipur 0 0, India$$;TIFR Centre For Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 0 0, India$$ | |
关键词: Spectral element method; vertex singularity; edge singularity; vertexedge singularity; modified coordinates; geometric mesh; quasi uniform mesh; stability estimate.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
This is the second of a series of papers devoted to the study of â„Ž-ð‘ spectral element methods for three dimensional elliptic problems on non-smooth domains. The present paper addresses the proof of the main stability theorem.We assume that the differential operator is a strongly elliptic operator which satisfies Lax–Milgram conditions. The spectral element functions are non-conforming. The stability estimate theorem of this paper will be used to design a numerical scheme which give exponentially accurate solutions to three dimensional elliptic problems on non-smooth domains and can be easily implemented on parallel computers.
【 授权许可】
Unknown
【 预 览 】
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RO201912040507156ZK.pdf | 344KB | download |