NDLI: Application of a 14-point averaging operator in the grid method

Content Provider	Springer Nature Link
Author	Volkov, E. A.
Copyright Year	2010
Abstract	The Dirichlet problem for Laplace’s equation in a rectangular parallelepiped is solved by applying the grid method. A 14-point averaging operator is used to specify the grid equations on the entire grid introduced in the parallelepiped. Given boundary values that are continuous on the parallelepiped edges and have first derivatives satisfying the Lipschitz condition on each parallelepiped face, the resulting discrete solution of the Dirichlet problem converges uniformly and quadratically with respect to the mesh size. Assuming that the boundary values on the faces have fourth derivatives satisfying the Hölder condition and the second derivatives on the edges obey an additional compatibility condition implied by Laplace’s equation, the discrete solution has uniform and quartic convergence with respect to the mesh size. The convergence of the method is also analyzed in certain cases when the boundary values are of intermediate smoothness.
Starting Page	2023
Ending Page	2032
Page Count	10
File Format	PDF
ISSN	09655425
Journal	Computational Mathematics and Mathematical Physics
Volume Number	50
Issue Number	12
e-ISSN	15556662
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2010-12-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	numerical solution of the Dirichlet problem for Laplace’s equation convergence of discrete solutions rectangular parallelepiped domain point averaging operator Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Computational Mathematics

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