Journal ArticleDOI
Error estimates for finite element method solution of the Stokes problem in the primitive variables
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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.read more
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.
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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.
Book ChapterDOI
Finite element methods for incompressible viscous flow
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
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.