Solving elliptical equations in 3D by means of an adaptive refinement in generalized finite differences
type: Item
instance of: scholarly article
title: Solving elliptical equations in 3D by means of an adaptive refinement in generalized finite differences
zbMATH Open document ID: 1427.65328
DOI: 10.1155/2018/9678473
author: Luis Gavete
author: Francisco Ureña
author: M. Ureña
author: M. Lucía Gavete
author: Juan José Benito
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We apply a 3D adaptive refinement procedure using meshless generalized finite difference method for solving elliptic partial differential equations. This adaptive refinement, based on an octree structure, allows adding nodes in a regular way in order to obtain smooth transitions with different nodal densities in the model. For this purpose, we define an error indicator as stop condition of the refinement, a criterion for choosing nodes with the highest errors, and a limit for the number of nodes to be added in each adaptive stage. This kind of equations often appears in engineering problems such as simulation of heat conduction, electrical potential, seepage through porous media, or irrotational flow of fluids. The numerical results show the high accuracy obtained.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 74S20
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 78M20
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35Q79
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 7019808
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9678473
OpenAlex ID: W2795133943
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Wikidata QID: Q130063320
description: scientific article; zbMATH DE number 7019808