Finite elements and the divergence constraint for viscous flows
Abstract
Chapter 1 introduces a technique, involving the concept of local divstability, for analyzing families of velocity/pressure trial spaces. Also, the technique is used to prove that various high order velocity/pressure families are divstable. Chapter 2 is concerned with the stability of certain families of low order spaces. The popular linear/constant box elements are shown to be unstable to order h and the notion of semistability is developed in an attempt to understand the observed behavior of these elements. In this chapter attention is confined to square grids. Chapter 3 includes additional examples of divstable velocity/pressure families and an application of the techniques of Chapter 2 to the linear/constant box elements on certain more general grids. Extensions of the type are desirable for interpreting the outputs from practical computer codes, most of which involve other than square regions, and moreover are needed for design of low degree optimal finite element schemes for solving the NavierStokes equations in velocity pressure formulation. The subject matter of this chapter will appear in a forthcoming article by the author and R. A. Nicolaides in the SIAM Journal of Numerical Analysis under the title, Stability of finite elements under divergence constraints.
 Publication:

Ph.D. Thesis
 Pub Date:
 1983
 Bibcode:
 1983PhDT........27B
 Keywords:

 Divergence;
 Finite Element Method;
 Velocity Measurement;
 Viscous Flow;
 Approximation;
 Computer Programs;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer