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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 12, Pages 2007–2023
DOI: https://doi.org/10.1134/S0044466919120081 (Mi zvmmf10993) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method

K. Gärtner, L. Kamenski

m4sim GmbH, Seydelstr. 31, Berlin, Germany
Citations (3)
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DOI: https://doi.org/10.1134/S0044466919120081
Abstract: Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the geometry of a problem and are able to preserve the essential qualitative properties of the solution for any given resolution in space and time as well as changes in time scales of multiple orders of magnitude. This work provides a brief description of the essential and useful properties of the Voronoi FVM, application examples, and a motivation why Voronoi FVM deserve to be used more often in practice than they are currently.
Key words: finite volume method, boundary conforming Delaunay triangulation, Voronoi cells.
Received: 26.06.2019
Revised: 26.06.2019
Accepted: 05.08.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 12, Pages 1930–1944
DOI: https://doi.org/10.1134/S096554251912008X
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: K. Gärtner, L. Kamenski, “Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method”, Zh. Vychisl. Mat. Mat. Fiz., 59:12 (2019), 2007–2023; Comput. Math. Math. Phys., 59:12 (2019), 1930–1944
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v59/i12/p2007
    • This publication is cited in the following 3 articles:
    1. Xiaoyu Jin, Benxi Liu, Shengli Liao, Chuntian Cheng, Zhipeng Zhao, Yi Zhang, “Robust Optimization for the Self-Scheduling and Bidding Strategies of a Hydroproducer Considering the Impacts of Crossing Forbidden Zones”, J. Water Resour. Plann. Manage., 149:2 (2023)  crossref
    2. Leonardo A. Poveda, Pedro Peixoto, “On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere”, Adv Comput Math, 49:3 (2023)  crossref
    3. V. A. Garanzha, L. Kamenski, L. N. Kudryavtseva, “Non-simplicial Delaunay meshing via approximation by radical partitions”, Comput. Math. Math. Phys., 62:8 (2022), 1203–1216  mathnet  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:27
     
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