Spectral Method and Spectral Element Method for Three Dimensional Linear Elliptic System: Analysis and Application

Arbaz Khan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, a least-squares spectral method and a non-conforming least-squares spectral element method for three dimensional linear elliptic system will be presented. Differentiability estimates and the main stability theorem for the proposed method are proven. Using the regularity estimate and the proposed stability estimates, we introduce a suitable preconditioner and show that the condition number of the preconditioned system is O((\ln W)^2) (where W is degree of polynomials). Then we establish the error estimates of the proposed method. Specific numerical results based on linear elasticity problem, fourth order problem and sixth order problem are discussed to reflect the efficiency of the proposed method.
Original languageEnglish
JournalJournal of Scientific Computing
Volume82
Issue number2
DOIs
Publication statusPublished - 6 Feb 2020

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