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 Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 286–297 (Mi zvmmf4828)

A modified combined grid method for solving the Dirichlet problem for the Laplace equation on a rectangular parallelepiped

E. A. Volkov

Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moskow, 119991 Russia

Abstract: A modified combined grid method is proposed for solving the Dirichlet problem for the Laplace equation on a rectangular parallelepiped. The six-point averaging operator is applied at next-to-the-boundary grid points, while the 18-point averaging operator is used instead of the 26-point one at the remaining grid points. Assuming that the boundary values given on the faces have fourth derivatives satisfying the Hölder condition, the boundary values on the edges are continuous, and their second derivatives obey a matching condition implied by the Laplace equation, the grid solution is proved to converge uniformly with the fourth order with respect to the mesh size.

Key words: numerical solution of the Dirichlet problem for Laplace’s equation, convergence of grid solutions, rectangular parallelepipedal domain.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 274–284

Bibliographic databases:

UDC: 519.633.2

Citation: E. A. Volkov, “A modified combined grid method for solving the Dirichlet problem for the Laplace equation on a rectangular parallelepiped”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 286–297; Comput. Math. Math. Phys., 50:2 (2010), 274–284

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. A. Volkov, “Application of a 14-point averaging operator in the grid method”, Comput. Math. Math. Phys., 50:12 (2010), 2023–2032
2. Comput. Math. Math. Phys., 52:6 (2012), 879–886
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