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Hierarchical basis in \(H^{\operatorname{div}}\) space for a mixed finite element formulation of the Darcy problem. (Russian. English summary) Zbl 1448.65248

Summary: 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 \(H^{\operatorname{div}}\) 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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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