Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations
Mathematics of Computation
Computer Methods in Applied Mechanics and Engineering
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering
Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations
SIAM Journal on Numerical Analysis
Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
A Finite Element Variational Multiscale Method for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
Stabilized finite element schemes with LBB-stable elements for incompressible flows
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Continuous Interior Penalty Finite Element Method for Oseen's Equations
SIAM Journal on Numerical Analysis
On the accuracy of the rotation form in simulations of the Navier-Stokes equations
Journal of Computational Physics
Short Note: New connections between finite element formulations of the Navier-Stokes equations
Journal of Computational Physics
A numerical method for mass conservative coupling between fluid flow and solute transport
Applied Numerical Mathematics
Hi-index | 0.01 |
We propose a stabilized mixed finite element method based on the Scott-Vogelius element for the Oseen equation. Here, only convection has to be stabilized since by construction both the discrete pressure and the divergence of the discrete velocities are controlled in the norm L^2. As stabilization we propose either the local projection stabilization or the interior penalty stabilization based on the penalization of the gradient jumps over element edges. We prove a discrete inf-sup condition leading to optimal a priori error estimates. Moreover, convergence of the velocities is completely independent of the pressure regularity, and in the purely incompressible case the discrete velocities are pointwise divergence free. The theoretical considerations are illustrated by some numerical examples.