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Journal ArticleDOI

Error estimates for finite element method solution of the Stokes problem in the primitive variables

Michel Bercovier, +1 more
- 01 Jun 1979 - 
- Vol. 33, Iss: 2, pp 211-224
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TLDR
In this article, error estimates for a class of finite element approximation of the Stokes equation are derived from a new Brezzi-type inequality for this kind of mixed formulation, which is true in 2 or 3 dimensions.
Abstract
In this paper we derive error estimates for a class of finite element approximation of the Stokes equation. These elements, popular among engineers, are conforming lagrangian both in velocity and pressure and therefore based on a mixed variational principle. The error estimates are established from a new Brezzi-type inequality for this kind of mixed formulation. The results are true in 2 or 3 dimensions.

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Citations
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Journal ArticleDOI

A stable finite element for the stokes equations

TL;DR: In this paper, a new velocity-pressure finite element for the computation of Stokes flow is presented, which satisfies the usual inf-sup condition and converges with first order for both velocities and pressure.
Journal ArticleDOI

On the transport-diffusion algorithm and its applications to the Navier-Stokes equations

TL;DR: An error bound is given that holds also for the Navier-Stokes equations even when the Reynolds number is infinite (Euler equation) and for thePDE in Lagrangian form.
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Computational vascular fluid dynamics: problems, models and methods

TL;DR: Three different issues are addressed in this paper: the definition of suitable mathematical models; the pre-processing of clinical data; and the development of appropriate numerical techniques.
Journal ArticleDOI

The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2

TL;DR: The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail and implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed.
References
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Journal ArticleDOI

On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers

Franco Brezzi
TL;DR: In this paper, the authors describe a fitting for hose end fittings that is suitable for use in conjunction with a cross-linked polyethylene hose or pipe, where a body incorporating a nipple adapted for insertion in a pipe end and a clamping ring normally retained on the body and adapted for clamping action about the outer surface of said pipe end is described.
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The solution of viscous incompressible jet and free-surface flows using finite-element methods

TL;DR: In this paper, a finite element program suitable for solving incompressible, viscous free surface problems in steady axisymmetric or plane flows is presented. But the authors do not consider the non-Newtonian flow, non-zero Reynolds numbers, and transient flow.
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A comparison of various mixed-interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations☆

TL;DR: In this paper, four types of mixed interpolation elements are considered and compared, namely, six-node triangular elements, eight-node serendipity elements, nine-node Lagrangian elements and four-node quadrilateral elements.