Query: heywood ranacher navier-stokes

title: Finite element approximation of the nonstationary Navier Stokes problem. I Regularity of solutions and second order error estimates for spatial discretization
abstract: This is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary Navier Stokes equations. Second order error estimates are proven for spatial discretization, using conforming or nonconforming elements. The results indicate a fluid like behavior of the approximations, even in the case of large data, so long as the solution remains regular. The analysis is based on sharp a priori estimates for the solution, particularly reflecting its behavior as$t \to 0$ and as $t \to \infty It is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the Navier Stokes equations, as it depends on nonlocal compatibility conditions for the data. The results which are presented here are independent of such compatibility conditions, which cannot be verified in practice.

title: Finite element approximation of the nonstationary Navier Stokes problem, part II: Stability of solutions and error estimates uniform in time
abstract: In this paper, assumptions about the stability of a solution are introduced in the numerical analysis of the nonstationary Navier Stokes problem, for the purpose of extending local a priori error estimates, and local a posteriori error estimates, globally in time.

title: Finite element approximations of the nonstationary Navier Stokes problem. Part IV: error estimates for second order time discretization
abstract: This paper provides an error analysis for the Crank Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier Stokes equations. Second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution. For approximations of an exponentially stable solution, these local error estimates are extended uniformly in time as \text{t} \to \infty

title: ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER STOKES EQUATIONS
abstract: Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby introducing artificial boundaries. Here we analyse out experience in choosing artificial boundary conditions implicitly through the choice of variational formulations. We deal particularly with a class of problems that involve the prescription of pressure drops and/or net flux conditions.

title: Finite element approximation of the nonstationary Navier Stokes problem, part III. Smoothing property and higher order error estimates for spatial discretization
abstract: This paper continues our error analysis of finite element Galerkin approximation of the nonstationary Navier Stokes equations. Optimal order error estimates, both local and global, are derived for higher order finite elements under appropriate assumptions about the smoothness and stability of the solution. These assumptions take into account the loss of regularity at $t 0$ that one generally has to expect in the absence of higher order nonlocal compatibility conditions for the data of the problem.

title: The exterior nonstationary problem for the Navier Stokes equations

title: On stationary solutions of the Navier Stokes equations as limits of nonstationary solutions

title: Existence of a Stationary Navier Stokes Flow Past a Rigid Body, with Application to Starting Problem in Higher Dimensions
abstract: We consider the large time behavior of the Navier Stokes flow past a rigid body in \mathbb{R}^n$ with $n\geq 3$ We first construct a small stationary solution possessing the optimal summability at spatial infinity, which is the same as that of the Oseen fundamental solution. When the translational velocity of the body gradually increases and is maintained after a certain finite time, we then show that the nonstationary fluid motion converges to the stationary solution corresponding to a small terminal velocity of the body as time $t\rightarrow\infty$ in $L^q$ with $q\in[n,\infty] This is called Finn's starting problem and the three dimensional case was affirmatively solved by Galdi, Heywood and Shibata (1997) The present paper extends their result to the case of higher dimensions. Even for the three dimensional case, our theorem provides new convergence rate, that is determined by the summability of the stationary solution at infinity and seems to be sharp.

title: An error estimate uniform in time for spectral Galerkin approximations of the Navier Stokes problem.

title: A Numerically Based Existence Theorem for the Navier Stokes Equations
abstract: We have recently experimented with a new spectral code for the spatially periodic nonstationary Navier Stokes equations, finding a plethora of apparently steady, periodic and chaotic solutions which seem interesting from the point of view of dynamical systems theory. This has stimulated our interest in the general problem of proving the existence of strict solutions of differential equations, that correspond to the computational results of numerical experiments. In this paper we analyze the numerical results of one of our experiments. The computational results appear to approximate what seems to be an unstable steady solution. Our objective is to provide a rigorous a posteriori analysis, proving that there does indeed exist a corresponding close by strict solution, and that it is steady. Our method is based on showing that the computed solution satisfies criteria which imply the convergence of a fixed point iteration, in appropriate function spaces for an existence theorem, using the computed solution as the starting value