Skip to main content

L-convergence of finite element approximations

Part of the Lecture Notes in Mathematics book series (LNM,volume 606)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. BREZIS, H., STAMPACCHIA, G.: Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France, 96, MR 39 No.659, 153–180 (1968).

    MathSciNet  MATH  Google Scholar 

  2. CIARLET, P.G., RAVIART, P.-A.: Interpolation Theory over Curved Elements, with Applications to Finite Element Methods. Comput. Methods in Appl. Mech. and Eng., 1, 217–249 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. CIARLET, P.G., RAVIART, P.-A.: Maximum Principle and Uniform Convergence for the Finite Element Method. Comput. Methods in Appl. Mech. and Eng., 2, 17–31 (1973).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. FALK, R.S.: Error Estimates for the Approximation of a Class of Variational Inequalities. Math. of Comp., 28, 963–971 (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. FALK, R.S.: Approximation of an Elliptic Boundary Value Problem with Unilateral Constraints. R.A.I.R.O. R2, 5–12 (1975).

    MathSciNet  MATH  Google Scholar 

  6. LIONS, J.L., STAMFACCHIA, G., Variational Inequalities. Comm. Pure Appl. Math., 20, 439–519 (1967).

    CrossRef  Google Scholar 

  7. NATTERER, F.: Über die punktweise Konvergenz finiter Elemente (to appear).

    Google Scholar 

  8. NATTERER, F.: Optimale L-Konvergenz finiter Elemente bei Variationsungleichungen (to appear).

    Google Scholar 

  9. NITSCHE, J.: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. d. Hamb. Math. Sem., 36, 9–15 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. NITSCHE, J.: On Approximation Methods for Dirichlet-Problems Using Subspaces with ‘Nearly-Zero’ Boundary Conditions. Proc. of a Conference "The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations." A.K. Aziz editor Academic Press, 603–627 (1972).

    Google Scholar 

  11. NITSCHE, J.: L-Convergence of Finite Element Approximation. 2. Conf. on Finite Elements, Rennes, France (1975).

    Google Scholar 

  12. SCOTT. R.: Optimal L-Estimates for the Finite Element Method on Irregular Meshes (to appear).

    Google Scholar 

  13. STRANG, G.: Finite Elements and Variational Inequalities. Seminaires Analyse Numérique, Paris (1973/74).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Nitsche, J. (1977). L-convergence of finite element approximations. In: Galligani, I., Magenes, E. (eds) Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol 606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064468

Download citation

  • DOI: https://doi.org/10.1007/BFb0064468

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08432-7

  • Online ISBN: 978-3-540-37158-8

  • eBook Packages: Springer Book Archive