Generalized difference methods for a nonlinear Dirichlet problem
SIAM Journal on Numerical Analysis
Some errors estimates for the box method
SIAM Journal on Numerical Analysis
Attractors for the penalized Navier-Stokes equations
SIAM Journal on Mathematical Analysis
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
On error estimates of the penalty method for unsteady Navier-Stokes equations
SIAM Journal on Numerical Analysis
Piecewise Linear Petrov--Galerkin Error Estimates For The Box Method
SIAM Journal on Numerical Analysis
Analysis and convergence of a covolume method for the generalized Stokes problem
Mathematics of Computation
On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computational Methods for Multiphase Flows in Porous Media (Computational Science and Engineering 2)
Computational Methods for Multiphase Flows in Porous Media (Computational Science and Engineering 2)
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
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A fully discrete penalty finite volume method is introduced for the discretization of the two-dimensional transient Navier-Stokes equations, where the temporal discretization is based on a backward Euler scheme and the spatial discretization is based on a finite volume scheme that uses a pair of P"2-P"0 trial functions on triangles. This method allows us to efficiently separate the computation of velocity from that of pressure with reasonably large time steps, and conserves mass locally. In addition, error estimates of optimal order are obtained for the fully discrete method under reasonable assumptions on temporal and spatial step sizes and the physical data. Finally, we present two numerical examples to illustrate the numerical algorithms developed and to show numerical results that agree with the theory established.