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

doi:10.1063/1.4965372

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

Mathematics

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

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 C^4,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 language	English
Article number	090008
Journal	AIP Conference Proceedings
Volume	1776
DOIs	https://doi.org/10.1063/1.4965372
Publication status	Published - 20 Oct 2016
Event	The 2nd International Conference Numerical Computations: Theory and Algorithms - Pizzo Calabro, Italy Duration: 19 Jun 2016 → 25 Jun 2016

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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{\textquoteright}s equation in a rectangular paralellepiped. It is proved that when the boundary functions on the faces of the rectangular parallelepiped are from the H{\"o}lder classes C4,λ, λ ∈ (0, 1), and their second and fourth derivatives obey compatibility conditions implied by Laplace{\textquoteright}s equation on the edges, the solution obtained by the constructed operator also has fourth-order accuracy with respect to mesh size.",

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year = "2016",

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doi = "10.1063/1.4965372",

language = "English",

volume = "1776",

journal = "AIP Conference Proceedings",

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AU - Celiker, Emine

AU - Dosiyev, Adiguzel

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Y1 - 2016/10/20

N2 - 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.

AB - 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.

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T2 - The 2nd International Conference Numerical Computations

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ER -

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

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