Finite element analysis of incompressible viscous flows by the penalty function formulation

Thomas J R Hughes; Wing Kam Liu; Alec Brooks

doi:10.1016/0021-9991(79)90086-X

Finite element analysis of incompressible viscous flows by the penalty function formulation

Thomas J R Hughes, Wing Kam Liu, Alec Brooks

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

472 Scopus citations

Abstract

A review of recent work and new developments are presented for the penalty-function/finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady Navier-Stokes equations. Galerkin and "upwind" treatments of convection terms are discussed. Numerical results indicate the versatility and effectiveness of the new methods.

Original language	English (US)
Pages (from-to)	1-60
Number of pages	60
Journal	Journal of Computational Physics
Volume	30
Issue number	1
DOIs	https://doi.org/10.1016/0021-9991(79)90086-X
State	Published - Jan 1979

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/0021-9991(79)90086-X

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title = "Finite element analysis of incompressible viscous flows by the penalty function formulation",

abstract = "A review of recent work and new developments are presented for the penalty-function/finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady Navier-Stokes equations. Galerkin and {"}upwind{"} treatments of convection terms are discussed. Numerical results indicate the versatility and effectiveness of the new methods.",

author = "Hughes, {Thomas J R} and Liu, {Wing Kam} and Alec Brooks",

note = "Funding Information: We wish to expresso ur gratitude to the Computer Center, California Institute of Technology, for providing computer funds, and to the National Science Foundation for providing support for two of us (W. K. L. and A. B.) under Grant ATA74-19135. We also wish to thank Dr. P. M. Gresho for suggestingt o the editors that we write the presenta rticle.",

year = "1979",

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doi = "10.1016/0021-9991(79)90086-X",

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AU - Hughes, Thomas J R

AU - Liu, Wing Kam

AU - Brooks, Alec

N1 - Funding Information: We wish to expresso ur gratitude to the Computer Center, California Institute of Technology, for providing computer funds, and to the National Science Foundation for providing support for two of us (W. K. L. and A. B.) under Grant ATA74-19135. We also wish to thank Dr. P. M. Gresho for suggestingt o the editors that we write the presenta rticle.

PY - 1979/1

Y1 - 1979/1

N2 - A review of recent work and new developments are presented for the penalty-function/finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady Navier-Stokes equations. Galerkin and "upwind" treatments of convection terms are discussed. Numerical results indicate the versatility and effectiveness of the new methods.

AB - A review of recent work and new developments are presented for the penalty-function/finite element formulation of incompressible viscous flows. Basic features of the penalty method are described in the context of the steady and unsteady Navier-Stokes equations. Galerkin and "upwind" treatments of convection terms are discussed. Numerical results indicate the versatility and effectiveness of the new methods.

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Finite element analysis of incompressible viscous flows by the penalty function formulation

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