TY - JOUR

T1 - On the fourth-order accurate approximations of the solution of the Dirichlet problem for Laplace’s equation in a rectangular parallelepiped

AU - Celiker, Emine

AU - Dosiyev, Adiguzel

PY - 2016/10/20

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.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-84995481238&origin=resultslist&sort=plf-f&src=s&st1=On+the+fourth-order+accurate+approximations+of+the+solution+of+the+Dirichlet+problem+for+Laplace%e2%80%99s+equation+in+a+rectangular+parallelepiped&sid=33d00a21f70f81fd150794d3c4c95a61&sot=b&sdt=b&sl=146&s=TITLE%28On+the+fourth-order+accurate+approximations+of+the+solution+of+the+Dirichlet+problem+for+Laplace%e2%80%99s+equation+in+a+rectangular+parallelepiped%29&relpos=0&citeCnt=0&searchTerm=

U2 - 10.1063/1.4965372

DO - 10.1063/1.4965372

M3 - Conference article

SN - 0094-243X

VL - 1776

JO - AIP Conference Proceedings

JF - AIP Conference Proceedings

M1 - 090008

T2 - The 2nd International Conference Numerical Computations

Y2 - 19 June 2016 through 25 June 2016

ER -