Some errors estimates for the box method
SIAM Journal on Numerical Analysis
On first and second order box schemes
Computing
The finite volume element method for diffusion equations on general triangulations
SIAM Journal on Numerical Analysis
Convergence of finite volume schemes for Poisson's equation on nonuniform meshes
SIAM Journal on Numerical Analysis
Analysis and convergence of the MAC scheme. II: Navier-Stokes equations
Mathematics of Computation
Analysis and convergence of a covolume method for the generalized Stokes problem
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
SIAM Journal on Numerical Analysis
| Hi-index | 0.00 |
We consider the discretization of the stationary Navier-Stokes system in a two-dimensional domain by a non-conforming finite volume element method. We use the standard formulation of the Navier-Stokes system in the primitive variables and take as approximation space the non-conforming P^1-elements for the velocity and piecewise constant elements for the pressure. The non-linear convective term is treated using an upstream approach with weight, based on the scheme from [F. Schieweck, L. Tobiska, A non-conforming finite element method of upstream type applied to the stationary Navier-Stokes equation, M^2AN 23 (1989) 627-647]. For the proposed scheme, we prove existence and uniqueness results (under the standard assumption that the datum has to be sufficiently small with respect to the viscosity parameter, cf. [R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1984]). An error estimate in the energy norm is proved and is confirmed by different numerical tests.