Skip to main content
SpringerLink
Log in
Book cover

Adaptive Methods — Algorithms, Theory and Applications pp 1–16Cite as

Galerkin/Least-Squares-FEM and Anisotropic Mesh Refinement

  • Chapter

  • 144 Accesses

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM))

Summary

The Galerkin /least-squares finite element method is considered as a tool for solving singularly perturbed partial differential equations of elliptic type on adaptively refined grids. Local error estimates in subdomains away from boundary and interior layers are uniformly valid with respect to the small parameter. Boundary and interior layers can be resolved using locally anisotropic mesh refinement. Numerical examples are given for scalar convection-diffusion equations and for incompressible Navier—Stokes flow problems.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • 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. Auge,A., Lube,G.: Regularized Mixed Finite Element Approximations of Incompressible Flow Problems. Preprint TU Magdeburg 1993.

    Google Scholar 

  2. Behr,M.: Stabilized Finite Element Methods for Incompressible Flows with Emphasis on Moving Boundaries and Interfaces. Thesis, Univ. of Minnesota 1992.

    Google Scholar 

  3. Guo,W., Stynes,M.: Pointwise Error Estimates for a Streamline Diffusion Scheme on a Shishkin Mesh for a Convection-Diffusion Problem. Preprint 1993–2, Dept. of Math., Univ. College. Cork, Ireland 1993.

    Google Scholar 

  4. EJ] Eriksson,K., Johnson,C.: Adaptive Streamline Diffusion Finite Element Methods for Convection-Diffusion Problems. Math. Comp.. (to appear).

    Google Scholar 

  5. Franca, L. P., Frey, S. L., Hughes, T. J. R.: Stabilized finite element methods. Part I. Comp. Meths. Appl. Mech. Engrg. 95 (1992), 253–276.

    Article  MathSciNet  MATH  Google Scholar 

  6. Johnson, C., Schatz, A. H., Wahlbin, L. B.: Crosswind Smear and Pointwise Errrors in Streamline Diffusion Finite Element Methods. Math. Comp. 49 (1987) 25–38.

    Article  MathSciNet  MATH  Google Scholar 

  7. Kornhuber,R., Roitzsch,R.: On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers. Preprint SC 89–5, K.Zuse-Zentrum Berlin (1989).

    Google Scholar 

  8. Lang,J.: An Adaptive Finite Element Method for Convec- tion-Diffusion Problems by Interpolation Techniques. Technical Report TR 91–4, K.Zuse-Zentrum Berlin 1991.

    Google Scholar 

  9. Lube,G.: Stabilized Galerkin Finite Element Methods for Convection Dominated and Incompressible Flow Problems. Proc. 37. Sem. Numer. Analysis and Math. Modell. 1991. Banach Center Public. Warsaw 1993.

    Google Scholar 

  10. Nävert,U.: A Finite Element Method for Convection-Diffusion Problems. Thesis, Chalmers Univ. Göteborg 1982

    Google Scholar 

  11. Shakib,F.: Finite Element Analysis of the Compressible Euler and Navier-Stokes Equations. Ph.D.Thesis Stan- ford Univ. 1989.

    Google Scholar 

  12. Shishkin,G. I.: Approximation of the solution of singularly perturbed boundary value problems with a parabolic boundary layer (Russ.). Sh.Vytsch.Matem. Mat.Fis. 29 (1989) 7, 963–977.

    MathSciNet  Google Scholar 

  13. WeiB,D.: Feldberechnungen mit der FEM zur Simulation von Temperatur- und Gefügeverteilungen bei Schweißprozessen. Forschungsbericht TU Magdeburg, GKMBI 1992

    Google Scholar 

  14. Zhou,G.: An Adaptive Streamline Diffusion Finite Element Method for Hyperbolic Systems in Gas Dynamics. Thesis, Univ. Heidelberg 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fluid Mech. Departm., Dresden Univ. of Technology, Mommsenstr.13, D-0-8027, Dresden, Germany

    A. Auge

  2. Math. Departm., Magdeburg Univ. of Technology, Postfach 4120, D-0-3010, Magdeburg, Germany

    G. Lube

  3. GKMBI, Magdeburg Univ. of Technology, Postfach 4120, D-0-3010, Magdeburg, Germany

    D. Weiß

Authors
  1. A. Auge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Lube
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Weiß
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wolfgang Hackbusch Gabriel Wittum

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Auge, A., Lube, G., Weiß, D. (1994). Galerkin/Least-Squares-FEM and Anisotropic Mesh Refinement. In: Hackbusch, W., Wittum, G. (eds) Adaptive Methods — Algorithms, Theory and Applications. Notes on Numerical Fluid Mechanics (NNFM). Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14246-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-663-14246-1_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07646-7

  • Online ISBN: 978-3-663-14246-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation