Covolume Solutions of Three-Dimensional Div-Curl Equations

Roy A. Nicolaides; Xiaonan Wu

doi:10.1137/S0036142994277286

Covolume Solutions of Three-Dimensional Div-Curl Equations

Roy A. Nicolaides, Xiaonan Wu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

56 Citations (Scopus)

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Abstract

The Voronoi-Delaunay mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. In this work, it is shown how such "covolume" discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration.

Original language	English
Pages (from-to)	2195-2203
Number of pages	9
Journal	SIAM Journal on Numerical Analysis
Volume	34
Issue number	6
DOIs	https://doi.org/10.1137/S0036142994277286
Publication status	Published - Nov 1997

Scopus Subject Areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Div-curl systems
Incompressible fluid dynamics
Partial differential equations

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10.1137/S0036142994277286

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abstract = "The Voronoi-Delaunay mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. In this work, it is shown how such {"}covolume{"} discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration.",

keywords = "Div-curl systems, Incompressible fluid dynamics, Partial differential equations",

author = "Nicolaides, {Roy A.} and Xiaonan Wu",

note = "Funding information: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 (rnom@andrew.cmu.edu). This author was supported by the United States Air Force Office of Scientific Research under grants F49620-92-J-0133 and F49620-94-0311. Publisher copyright: Copyright {\textcopyright} 1997 Society for Industrial and Applied Mathematics",

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AU - Wu, Xiaonan

N1 - Funding information: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 (rnom@andrew.cmu.edu). This author was supported by the United States Air Force Office of Scientific Research under grants F49620-92-J-0133 and F49620-94-0311. Publisher copyright: Copyright © 1997 Society for Industrial and Applied Mathematics

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N2 - The Voronoi-Delaunay mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. In this work, it is shown how such "covolume" discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration.

AB - The Voronoi-Delaunay mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. In this work, it is shown how such "covolume" discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration.

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KW - Incompressible fluid dynamics

KW - Partial differential equations

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ER -

Covolume Solutions of Three-Dimensional Div-Curl Equations

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