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

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/125/03/0413-0447

• # Keywords

Spectral element method; vertex singularity; edge singularity; vertexedge singularity; modified coordinates; geometric mesh; quasi uniform mesh; stability estimate.

• # Abstract

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.

• # Author Affiliations

1. Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur 208 016, India
2. Department of Mathematics, The LNM Institute of Information Technology, Jaipur 302 031, India
3. TIFR Centre For Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560 065, India
4. Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019