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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1741–1765
DOI: https://doi.org/10.33048/semi.2020.17.119 (Mi semr1313) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Computational mathematics

Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the Darcy problem

S. A. Trofimovaab, N. B. Itkinab, È. P. Shurinaab

a Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, 3, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State Technical University, 20, K. Marksa ave., Novosibirsk, 630073, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.119
Abstract: A mixed variational formulation based on a discontinuous Galerkin method for solving the Darcy problem with a tensor permeability coefficient is considered. Two special hierarchical basis systems in $H^{div}$ space for velocity and in $H^1$ space for pressure are constructed. The influence of these basis on the properties of the matrix of the discrete analogue is investigated.
Keywords: mixed variational formulation, discontinuous Galerkin method, Darcy problem, algebraic multilevel method.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0331-2019-0015
0266-2019-0007
Russian Foundation for Basic Research 16-29-15094
Received April 16, 2019, published October 26, 2020
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 35Q04
Language: Russian
Citation: S. A. Trofimova, N. B. Itkina, È. P. Shurina, “Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the Darcy problem”, Sib. Èlektron. Mat. Izv., 17 (2020), 1741–1765
Citation in format AMSBIB
\Bibitem{TroItkShu20}
\by S.~A.~Trofimova, N.~B.~Itkina, \`E.~P.~Shurina
\paper Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the Darcy problem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1741--1765
\mathnet{http://mi.mathnet.ru/semr1313}
\crossref{https://doi.org/10.33048/semi.2020.17.119}
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