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Weight Uniform Accuracy Estimates of Finite Difference Method for Poisson Equation, Taking into Account Boundary Effect

  • V. L. Makarov
  • L. I. Demkiv
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

Poisson equation in polyhedral domain Ω ⊂ R n , n = 2,3 with boundary Γ, when Dirichlet conditions are given on all faces or on all but one where Neimann conditions are given, is considered.

Traditional difference schemes with semi-constant steps along axes precisely approximate Dirichlet conditions hence it is expected that their accuracy order increases approaching to corresponding part of boundary γ. This paper is dedicated to quantitative investigation of this boundary effect. It is also shown that analogous boundary effect in the mesh knots takes place also for finite-element method (super convergence).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • V. L. Makarov
    • 1
  • L. I. Demkiv
    • 2
  1. 1.Institute of Mathematics of Ukrainian National Academy of SciencesKyivUkraine
  2. 2.National University, Lvivska PolytechnicaUkraine

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