ℎ-𝑝 Spectral element methods for three dimensional elliptic problems on non-smooth domains, Part-II: Proof of stability theorem

Proceedings Mathematical Sciences

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 ℎ-𝑝 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