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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
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.
Received April 16, 2019, published October 26, 2020
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
Linking options:
https://www.mathnet.ru/eng/semr1313 https://www.mathnet.ru/eng/semr/v17/p1741
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