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Article
Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations
In this article, we present a new fully discrete finite element nonlinear Galerkin method, which are well suited to the long time integration of the Navier-Stokes equations. Spatial discretization is based on...
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Article
Numerical analysis of a modified finite element nonlinear Galerkin method
A fully discrete modified finite element nonlinear Galerkin method is presented for the two-dimensional equation of Navier-Stokes type. The spatial discretization is based on two finite element spaces X ...
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Article
Asymptotic behavior and time discretization analysis for the non-stationary Navier-Stokes problem
The asymptotic behavior and the Euler time discretization analysis are presented for the two-dimensional non-stationary Navier-Stokes problem. If the data ν and f(t) satisfy a...
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Article
Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization
A multi-level spectral Galerkin method for the two-dimensional non-stationary Navier-Stokes equations is presented. The method proposed here is a multiscale method in which the fully nonlinear Navier-Stokes eq...
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Article
Local and parallel finite element algorithms for the stokes problem
Based on two-grid discretizations, some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed in this paper. These algorithms are motivated by the observation that for a...
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Article
A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier–Stokes equations
This paper proposes and analyzes a stabilized multi-level finite volume method (FVM) for solving the stationary 3D Navier–Stokes equations by using the lowest equal-order finite element pair without relying on...
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Article
Euler implicit/explicit iterative scheme for the stationary Navier–Stokes equations
In this paper, a new uniqueness assumption (A2) of the solution for the stationary Navier–Stokes equations is presented. Under assumption (A2), the exponential stability of the solution