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Numerische Mathematik

, Volume 44, Issue 2, pp 223–232 | Cite as

On the convergence of difference schemes for the approximation of solutionsu ∈ W 2 m (m>0.5) of elliptic equations with mixed derivatives

  • Rajčo D. Lazarov
  • Vladimir L. Makarov
  • Wilfried Weinelt
Article

Summary

The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu ∈ W 2 m (Ω),m>0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW 2 s (ω), ω denoting the set of grid points, is shown to be of the orderO(|h|m−s), 0≦s<m.

Subject Classifications

AMS: 65N10 CR: 5.17 

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Rajčo D. Lazarov
    • 1
  • Vladimir L. Makarov
    • 2
  • Wilfried Weinelt
    • 3
  1. 1.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Kiev State UniversityKievUSSR
  3. 3.Sektion Mathematik der Technischen Hochschule Karl-Marx-StadtKarl-Marx-StadtGerman Democratic Republic

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