Geodesic
Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the Darcy problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1741-1765

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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. 
@article{SEMR_2020_17_a122,
     author = {S. A. Trofimova and N. B. Itkina and \`E. P. Shurina},
     title = {Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the {Darcy} problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1741--1765},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a122/}
}
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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. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1741-1765. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a122/