To read this content please select one of the options below:

On the convergence of incompressible finite element formulations: The Patch Test and the inf‐sup condition

Eduardo N. Dvorkin (Center for Industrial Research, FUDETEC, Buenos Aires, Argentina)

Engineering Computations

ISSN: 0264-4401

Article publication date: 1 May 2001

463

Abstract

Engineers have developed robust and efficient incompressible finite element formulations using tools such as the Patch Test and the counting of constraints/variables, the first one aimed at the development of consistent elements and the second one aimed at the development of non‐locking and stable elements. The mentioned tools are rooted in the physics of the continuum mechanics problem. Mathematicians, on the other side, developed complex and powerful tools to examine the convergence of finite element formulations, such as the inf‐sup condition, these methods are based on the properties of the elliptical PDEs that constitute the mathematical model of the continuum mechanics problem. In this paper we intend to understand the inf‐sup condition from an engineering perspective, so as to be able to incorporate it into the package of tools used in the development of finite element formulations.

Keywords

Citation

Dvorkin, E.N. (2001), "On the convergence of incompressible finite element formulations: The Patch Test and the inf‐sup condition", Engineering Computations, Vol. 18 No. 3/4, pp. 539-556. https://doi.org/10.1108/02644400110387145

Publisher

:

MCB UP Ltd

Copyright © 2001, MCB UP Limited

Related articles