Advertisement

Numerische Mathematik

, Volume 52, Issue 5, pp 523–537 | Cite as

A quantitative discrete H2-regularity estimate for the Shortley-Weller scheme in convex domains

  • Winfried Auzinger
Article
  • 47 Downloads

Summary

We investigate the discreteH2-regularity properties of the Shortley-Weller discretization of Poisson's equation (with homogeneous Dirichlet boundary condition) in bounded convex domains Ω⊂ℝ2. It is shown that the regularity constant is 1 independent of the mesh sizeh if theH2-seminorm is defined in a way assigning less weight to the (unsymmetric) differences near the boundary.

Subject Classifications

AMS(MOS): 65N99 CR: G1.8 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Auzinger, W.: Defect corrections for multigrid solutions of the Dirichlet problem in general domains. Math. Comput.48, 471–484 (1987)Google Scholar
  2. 2.
    Dryja, M.: Prior estimates inW 2 2 in a convex domain for systems of elliptic difference equations. Zh. Vychisl. Mat. Mat. Fiz.12, 1595–1601 (1972)Google Scholar
  3. 3.
    Hackbusch, W.: Multi-Grid Methods and Applications. Springer Series in Computational Mathematics4 (1985)Google Scholar
  4. 4.
    Hackbusch, W.: On the regularity of difference schemes. Part II: Regularity estimates for linear and nonlinear problems. Arkiv för matematik21, 3–28 (1983)Google Scholar
  5. 5.
    Ladyzhenskaya, O.A.: The Boundary Value Problems of Mathematical Physics. Springer Applied Mathematical Sciences 49 (1985)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Winfried Auzinger
    • 1
  1. 1.Institut für Angewandte und Numerische MathematikTechnische Universität WienWienAustria

Personalised recommendations