A stabilized finite element method for the time-dependent Stokes equations based on Crank–Nicolson Scheme

Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations

This paper provides an error analysis for the Crank–Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier–Stokes problem, where the finite element space pair (Xh,Mh) for the approximation (uh, p n h) of the velocity u and the pressure p is constructed by the low-order finite ele...

A fully discrete stabilized finite element method for the time-dependent Navier-Stokes equations

In this article, we consider a fully discrete stabilized finite element method based on two local Gauss integrations for the two-dimensional time-dependent Navier–Stokes equations. It focuses on the lowest equal-order velocity–pressure pairs. Unlike the other stabilized method, the present approach does not require specification of a stabilization parameter or calculation of higher-order deriva...

A Stabilized Finite Element Scheme for the Navier-stokes Equations on Quadrilateral Anisotropic Meshes

It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori err...

An Iterative Substructuring Method for the Discretized Stokes Equations by a Stabilized Finite Element Method

Abstract. A simple algorithm of iterative substructuring method as the same way of elasticity problem is proposed for a discretized Stokes equation by P1/P1 element and penalty stabilization technique. Owing to the stability term, solvabilities of local Dirichlet problem, of local Neumann problem for preconditioner, and of the coarse space problem are ensured. Conjugate gradient method with pre...

An Adaptive Finite Element Method for the Incompressible Navier{stokes Equations on Time-dependent Domains