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Finite volume methods on Voronoi meshes
Author(s) -
Mishev Ilya D.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199803)14:2<193::aid-num4>3.0.co;2-j
Subject(s) - voronoi diagram , polygon mesh , mathematics , finite volume method , norm (philosophy) , centroidal voronoi tessellation , finite difference , partial differential equation , stability (learning theory) , finite element method , mathematical optimization , mathematical analysis , geometry , computer science , mechanics , physics , machine learning , political science , law , thermodynamics
Two cell‐centered finite difference schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H 1 ‐norm for both symmetric and nonsymmetric problems, including convection dominated, are proven. The theoretical results are illustrated with several numerical experiments. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:193–212, 1998