Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Quasi-Optimal Nonconforming Methods for Second-Order Problems on Domains with Non-Lipschitz Boundary

Authors : Andreas Veeser, Pietro Zanotti

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We introduce new nonconforming finite element methods for elliptic problems of second order. In contrast to previous work, we consider mixed boundary conditions and the domain does not have to lie on one side of its boundary. Each method is quasi-optimal in a piecewise energy norm, thanks to the discretization of the load functional with a moment-preserving smoothing operator.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

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

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

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




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

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




Jetzt Wissensvorsprung sichern!

inform now
previous chapter An Introduction to the Gradient Discretisation Method
next chapter Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation
Literature
1.
D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19(4), 742–760 (1982)MathSciNetCrossRef
2.
P. Ciarlet Jr., C.F. Dunkl, S. Sauter, A family of Crouzeix-Raviart finite elements in 3D, arXiv:1703.03224v1 [math.NA]
3.
P. Hansbo, M.G. Larson, Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity. M2AN Math. Model. Numer. Anal. 37, 63–72 (2003)
4.
B. Rivière, M.F. Wheeler, V. Girault, A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39, 902–931 (2001)MathSciNetCrossRef
5.
A. Veeser, Approximating gradients with continuous piecewise polynomial functions. Found. Comput. Math. 16(3), 723–750 (2016)MathSciNetCrossRef
6.
7.
A. Veeser, P. Zanotti, Quasi-optimal nonconforming methods for symmetric elliptic problems. II – Overconsistency and classical nonconforming elements, arXiv:1710.03447 [math.NA]
8.
A. Veeser, P. Zanotti, Quasi-optimal nonconforming methods for symmetric elliptic problems. III – DG and other interior penalty methods, SIAM J. Numer. Anal. (accepted for publication)
Metadata
Title
Quasi-Optimal Nonconforming Methods for Second-Order Problems on Domains with Non-Lipschitz Boundary
Authors
Andreas Veeser
Pietro Zanotti
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_41

Premium Partner

    Image Credits