Computer Methods in Applied Mechanics and Engineering
Attractors for the penalized Navier-Stokes equations
SIAM Journal on Mathematical Analysis
Computer Methods in Applied Mechanics and Engineering
On error estimates of the penalty method for unsteady Navier-Stokes equations
SIAM Journal on Numerical Analysis
A Two-Level Method with Backtracking for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations
SIAM Journal on Numerical Analysis
A Finite Element Variational Multiscale Method for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
SIAM Journal on Numerical Analysis
A stabilized finite element method based on two local Gauss integrations for the Stokes equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A new stabilized finite element method for shape optimization in the steady Navier--Stokes flow
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Stabilized finite element method for the viscoelastic Oldroyd fluid flows
Numerical Algorithms
Two-level stabilized method based on three corrections for the stationary Navier-Stokes equations
Applied Numerical Mathematics
Mathematics and Computers in Simulation
On the semi-discrete stabilized finite volume method for the transient Navier---Stokes equations
Advances in Computational Mathematics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
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This article considers a stabilized finite element approximation for the branch of nonsingular solutions of the stationary Navier-Stokes equations based on local polynomial pressure projection by using the lowest equal-order elements. The proposed stabilized method has a number of attractive computational properties. Firstly, it is free from stabilization parameters. Secondly, it only requires the simple and efficient calculation of Gauss integral residual terms. Thirdly, it can be implemented at the element level. The optimal error estimate is obtained by the standard finite element technique. Finally, comparison with other methods, through a series of numerical experiments, shows that this method has better stability and accuracy.