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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Makarov, V.L., Demkiv, L.I. (2009). Weight Uniform Accuracy Estimates of Finite Difference Method for Poisson Equation, Taking into Account Boundary Effect. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_9
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DOI: https://doi.org/10.1007/978-3-642-00464-3_9
Publisher Name: Springer, Berlin, Heidelberg
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