Exponentially accurate spectral element method for fourth order elliptic problems

• Verfasst von: Khan, Arbaz [VerfasserIn]
• Verfasst von: Husain, Akhlaq [VerfasserIn]
• Titel: Exponentially accurate spectral element method for fourth order elliptic problems
• Verf.angabe: Arbaz Khan, Akhlaq Husain
• Jahr: 2017
• Jahr des Originals: 2016
• Umfang: 26 S.
• Fussnoten: Published online: 04 October 2016 ; Gesehen am 16.08.2018
• Titel Quelle: Enthalten in: Journal of scientific computing
• Ort Quelle: New York, NY [u.a.] : Springer Science + Business Media B.V., 1986
• Jahr Quelle: 2017
• Band/Heft Quelle: 71(2017), 1, Seite 303-328
• ISSN Quelle: 1573-7691
• DOI: doi:10.1007/s10915-016-0300-z
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1580095364

Abstract

In this paper, a fully non-conforming least-squares spectral element method for fourth order elliptic problems on smooth domains is presented. The proposed method works for a general fourth order elliptic operator with non-homogeneous data in two dimensions and gives exponentially accurate solutions. We derive differentiability estimates and prove our main stability estimate theorem using a non-conforming spectral element method. We then formulate a numerical scheme using a block diagonal preconditioner. Error estimates are also proven for the proposed method. We provide the computational complexity of our method and present results of numerical simulations that have been performed to validate the theory.