Computing

, Volume 82, Issue 1, pp 1–9 | Cite as

Anisotropic error estimates for an interpolant defined via moments

  • G. Acosta
  • Thomas Apel
  • R. G. Durán
  • A. L. Lombardi
Article

Summary

An interpolant defined via moments is investigated for triangles, quadrilaterals, tetrahedra, and hexahedra and arbitrarily high polynomial degree. The elements are allowed to have diameters with different asymptotic behavior in different space directions. Anisotropic interpolation error estimates are proved.

AMS Subject Classifications

65D05 65N30 

Keywords

anisotropic finite elements interpolation error estimate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Apel T. (1999). Anisotropic finite elements: local estimates and applications. Teubner, Stuttgart Google Scholar
  2. 2.
    Apel T. and Dobrowolski M. (1992). Anisotropic interpolation with applications to the finite element method. Computing 47: 277–293 CrossRefMathSciNetGoogle Scholar
  3. 3.
    Apel, T., Matthies, G.: Non-conforming, anisotropic, rectangular finite elements of arbitrary order for the Stokes problem. SIAM J Numer Anal (forthcoming)Google Scholar
  4. 4.
    Buffa A., Costabel M. and Dauge M. (2005). Algebraic convergence for anisotropic edge elements in polyhedral domains. Numer Math 101: 29–65 MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Girault V. and Raviart P.-A. (1986). Finite element methods for Navier–Stokes equations. Springer, Berlin MATHGoogle Scholar
  6. 6.
    Lin, Q., Yan, N., Zhou, A.: A rectangle test for interpolated finite elements. In: Proc. of Sys. Scit. and Sys. Engng., Great Wall (Hong Kong), pp. 217–229, Culture Publish Co. (1991)Google Scholar
  7. 7.
    Mao, S., Shi, Z.-C.: Error estimates for triangular finite elements satisfying a weak angle condition. Sci China, Ser A (2007)Google Scholar
  8. 8.
    Stynes, M., Tobiska, L.: Using rectangular \({\mathcal{Q}}_{p}\) elements in the sdfem for a convection–diffusion problem with a boundary layer. Appl Numer Math (forthcoming)Google Scholar
  9. 9.
    Zhou A. and Li J. (1994). The full approximation accuracy for the stream function–vorticity–pressure method. Numer Math 68: 427–435 MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2008

Authors and Affiliations

  • G. Acosta
    • 1
  • Thomas Apel
    • 2
  • R. G. Durán
    • 3
  • A. L. Lombardi
    • 3
  1. 1.Instituto de CienciasUniversidad Nacional de General SarmientoLos PolvorinesArgentina
  2. 2.Institut für Mathematik und BauinformatikUniversität der Bundeswehr MünchenNeubibergGermany
  3. 3.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

Personalised recommendations