Implementation of Finite Element Methods for Navier-Stokes Equations

Abstract

Library of Congress Cataloging in PublicationData Thomasset, Frani,(ois. Implementation of finite element for Navier-Stokes equations. (Springer series in computational physics) I. Fluid dynamics. 2. Navier-Stokes equations-Numerical solutions. 3. Finite element method. I. Title. II. Series. QA911.T46 515.3'53 81-9169 AACR2

On the approximation of the spectrum of the Stokes operator

“…Thanks to (14), P z > h {{ul*, ..., uf* h ) ) c V h is /-dimensional for sufficiently small e (as in Strang and Fix [11], proof of Lemma 6.1, page 229), « sufficiently small » being independent of h, by (13) and (14). Therefore we obtain from (17), again by the max-min principle, so that…”

“…Let Q h c L 2 (ft) be another finite dimensional space. We set a(.u,v) = vj | ^£ d *> u,ve( An approximation to the solution (u,p) of (1) The computation of {>^}jti may be carried out within the self-adjoint framework if a basis for V h is available (see, for example, [6], [7], [14]). Otherwise we may consider a regularized version of (2) This formulation has been quite popular in recent years.…”

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

“…For a simply connected Ω, there exists a completely local basis for V h consisting of vector fields tangential to the edges of T h and vector fields representing rotations around the vertices of T h [18,10]. For a multiply connected domain, the basis of V h involves vector fields along cuts that reduce Ω to a simply connected domain, in addition to local vector fields.…”

Modeling, Simulation and Optimization of Electrorheological Fluids

“…Time-dependent problems shall be taken care of in 3.2, and in 3.3 we shall address non-isothermal fluid flows. We refer to CROCHET [1984], ELMAN, SILVESTER and WATHEN [2005], GLOWINSKI [2004], GUNZBURGER [1989], HUANG [1998], THOMASSET [1981], TUREK [1999] with regard to a general presentation of numerical solution techniques for Newtonian and nonNewtonian fluid flows.…”