Newton's method for the Navier-Stokes equations with finite-element initial guess of stokes equations

Newton's method for the Navier-Stokes equations with finite-element initial guess of stokes equations

K e y w o r d s N a v i e r S t o k e s equations, Stokes equations, Convergence, Finite element method, Newton's method. 1. I N T R O D U C T I O N In the course of so lv ing non l inear equa t ions like Navie r -S tokes equa t ions , one m a y e m p l o y N e w t o n and Newtonl ike m e t h o d s combin ing wi th o the r m e t h o d s (see, for example , [1-3], etc.) . I t is well known t h a...

A Mixed Finite Element Method for Navier-stokes Equations

This paper describes a numerical solution of Navier-Stokes equations. It includes algorithms for discretization by finite element methods and a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like ADINA system. AMS Mathemat...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Comparison of Finite Element Methods for the Navier-Stokes Equations

A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations

Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier–Stokes equations, along with a piecewiseconstant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for t...