Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

01-04-2014 | Issue 1/2014

Journal of Scientific Computing 1/2014

Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes

Journal:
Journal of Scientific Computing > Issue 1/2014
Authors:
Xuying Zhao, Zhong-Ci Shi, Qiang Du

Abstract

Finite element methods (FEMs) on nonconforming meshes have been much studied in the literature. In all earlier works on such methods , some constraints must be imposed on the degrees of freedom on the edge/face with hanging nodes in order to maintain continuity, which make the numerical implementation more complicated. In this paper, we present two FEMs on quadrilateral nonconforming meshes which are constraint-free. Furthermore, we establish the corresponding residual-based a posteriori error reliability and efficiency estimation for general quadrilateral meshes. We also present extensive numerical testing results to systematically compare the performance among three adaptive quadrilateral FEMs: the constraint-free adaptive \(\mathbb Q _1\) FEM on quadrilateral nonconforming meshes with hanging nodes developed herein, the adaptive \(\mathbb Q _1\) FEM based on quadrilateral red-green refinement without any hanging node recently proposed in Zhao et al. (SIAM J Sci Comput 3(4):2099–2120, 2010), and the classical adaptive \(\mathbb Q _1\) FEM on quadrilateral nonconforming meshes with constraints on hanging nodes. Some extensions are also included in this paper.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Maschinenbau + Werkstoffe​​​​​​​




Testen Sie jetzt 30 Tage kostenlos.

Literature
About this article

Other articles of this Issue 1/2014

Journal of Scientific Computing 1/2014 Go to the issue

Premium Partner

    Image Credits