Spline-interpolation solution of 3D Dirichlet problem for a certain class of solids
type: Item
instance of: scholarly article
title: Spline-interpolation solution of 3D Dirichlet problem for a certain class of solids
zbMATH Open document ID: 1287.65108
published in: IMA Journal of Applied Mathematics
publication date: 2014-01-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1103.3830
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6251138
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: numerical examples
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: spline-interpolation method
zbMATH Keywords: error estimate
author: P. N. Ivanshin
author: E. A. Shirokova
MaRDI profile type: Publication
OpenAlex ID: W2069273122
arXiv ID: 1103.3830
DOI: 10.1093/IMAMAT/HXS009
review text: The authors present a spline-interpolation approximate solution of the Dirichlet problem for the Laplace equation in axisymmetric domains. The spline-interpolation method is the analogue of the finite element method where instead of the boundary nodes one considers the closed boundary curves and introduces the cells as the layers between two parallel planes. So, the 3D problem is reduced to a sequence of 2D Dirichlet problems. The main advantage of the spline-interpolation solution is its continuity in the whole domain up to the boundary. An error estimate of the problem is obtained.The spline-interpolation solution presented in the paper is also applied to the Dirichlet problem for a cylinder or a cone with the section which is the known conformal map of the unit disc. Some examples illustrate the theory.
reviewed by: Adrian Carabineanu
description: scientific article; zbMATH DE number 6251138