Analysis of a unified stabilized finite volume method for the Darcy-Stokes problem. (Chinese. English summary) Zbl 1240.76033
Summary: A unified stabilized finite volume element method is proposed for the Darcy-Stokes problem. For the discretization form, two grids are needed; one is triangulation and the other is a quadrilateral mesh. The velocity is approximated using nonconforming piecewise linear and pressure piecewise constants. The proposed unified method in this paper is shown to be stable and optimally convergent for both velocity and pressure. Moreover, numerical experiments are given to demonstrate the theoretical results.
MSC:
76M12 | Finite volume methods applied to problems in fluid mechanics |
65N08 | Finite volume methods for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |