On the fourth-order accurate approximations of the solution of the Dirichlet problem for Laplace’s equation in a rectangular parallelepiped

Emine Celiker, Adiguzel Dosiyev

Research output: Contribution to journalConference articlepeer-review

Abstract

An interpolation operator is proposed using the cubic grid solution of order O(h4), h is the mesh size, of the Dirichlet problem for Laplace’s equation in a rectangular paralellepiped. It is proved that when the boundary functions on the faces of the rectangular parallelepiped are from the Hölder classes C4,λ, λ ∈ (0, 1), and their second and fourth derivatives obey compatibility conditions implied by Laplace’s equation on the edges, the solution obtained by the constructed operator also has fourth-order accuracy with respect to mesh size.
Original languageEnglish
Article number090008
JournalAIP Conference Proceedings
Volume1776
DOIs
Publication statusPublished - 20 Oct 2016
EventThe 2nd International Conference Numerical Computations: Theory and Algorithms - Pizzo Calabro, Italy
Duration: 19 Jun 201625 Jun 2016

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