Skip to main content

A-posteriori error estimates. Adaptive local mesh refinement and multigrid iteration

Part of the Lecture Notes in Mathematics book series (LNM,volume 1228)

Keywords

  • Posteriori Error
  • Posteriori Error Estimate
  • Finite Element Space
  • Nonuniform Mesh
  • Adaptive Refinement

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

References

  1. Babuska, I. and A. Miller, A posteriori error estimates and adaptive techniques for the finite element method. Technical Report BN-968, Institute for Physical Sciences and Technology, University of Maryland, 1981.

    Google Scholar 

  2. Babuska, I. and W. C. Rheinboldt, A posteriori error analysis of finite element solutions or one-dimensional problems. SIAM Journal on Numerical Analysis 18:565–589, 1981.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Babuska, I. and W. C. Rheinboldt, A posteriori error estimates for the finite element method. International Journal for Numerical Methods in Engineering 12:1597–1615, 1978.

    CrossRef  MATH  Google Scholar 

  4. Babuska, I. and W. C. Rheinboldt, Analysis of optimal finite-element meshes in R1. Mathematics of Computation 33:435–463, 1979.

    MathSciNet  MATH  Google Scholar 

  5. Babuska, I. and W. C. Rheinboldt, Error estimates for adaptive finite element computations. SIAM Journal on Numerical Analysis 15:736–754, 1978.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Babuska, I. and W. C. Rheinboldt, On the reliability and optimality of the finite element method. Computer and Structures 10:87–94, 1979.

    CrossRef  MATH  Google Scholar 

  7. Babuska, I. and W. C. Rheinboldt, Reliable error estimation and mesh adaptation for the finite element method. In Computational Methods in Nonlinear Mechanics, 67–108, North-Holland, New York, 1980.

    Google Scholar 

  8. Bank, R. E., PLTMG User's Guide, Edition 4.0. Technical Report, Department of Mathematica, University of California at San Diego, La Jolla, California, March, 1985.

    Google Scholar 

  9. Bank, R. E. and C. Douglas, Sharp estimates for multigrid rates of convergence with general smoothing and acceleration. SIAM Journal of Numerical Analysis 22:617–633 (1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Bank, R. E., A. H. Sherman, and A. Weiser, Refinement algorithms and data structures for regular local mesh refinement. In Scientific Computing, R. Stepleman et al., Eds., IMACS/North-Holland, New York, 3–17, 1983.

    Google Scholar 

  11. Bank, R. E. Analysis of a local a-posteriori error estimate for elliptic equations. In Accuracy Estimates and Adaptive Refinement in Finite Element Computations, Babuska et al., Eds., John Wiley, 1985.

    Google Scholar 

  12. Bank, R. E. and A. Weiser, Some a posteriori error estimates for elliptic partial differential equations. Mathematics of Computation, 44:283–301, 1985.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Elman, H. C., Iterative Methods for Large Sparse Nonsymmetric Systems of Linear Equations. Technical Report 229, Computer Science Department, Yale University, 1982.

    Google Scholar 

  14. Weiser, A., Local-mesh, local-order, adaptive finite element methods with a posteriori error estimators for elliptic partial differential equations. Technical Report 213, Computer Science Department, Yale University, 1981.

    Google Scholar 

  15. Yserentant, Y., On the Multi-level Splitting of Finite Element Spaces. Technical Report 21, University of Aachen, 1983.

    Google Scholar 

  16. Yserentant, Y., The Convergence of Multi-level Methods for Solving Finite Element Equations in the Presence of Singularities. Technical Report 14, University ofAachen, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Bank, R.E. (1986). A-posteriori error estimates. Adaptive local mesh refinement and multigrid iteration. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods II. Lecture Notes in Mathematics, vol 1228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072638

Download citation

  • DOI: https://doi.org/10.1007/BFb0072638

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17198-0

  • Online ISBN: 978-3-540-47372-5

  • eBook Packages: Springer Book Archive