Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
Joint Authors
Gavete, Luis
Gavete, María Lucía
Benito, Juan José
Ureña, Francisco
Ureña, Miguel
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-27
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Gavete, Luis& Ureña, Francisco& Benito, Juan José& Ureña, Miguel& Gavete, María Lucía. 2018. Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1209755
Modern Language Association (MLA)
Gavete, Luis…[et al.]. Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences. Mathematical Problems in Engineering No. 2018 (2018), pp.1-14.
https://search.emarefa.net/detail/BIM-1209755
American Medical Association (AMA)
Gavete, Luis& Ureña, Francisco& Benito, Juan José& Ureña, Miguel& Gavete, María Lucía. Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1209755
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209755