The penalty method for the Navier-Stokes equations

SummaryThe penalty finite element method as it applies to the Stokes and Navier-Stokes flow equations is reviewed. The main developments are discussed and selected but still extensive list of references is provided.

[1]  R. Sani,et al.  Solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method , 1981 .

[2]  Graham F. Carey,et al.  Continuation techniques for a penalty approximation of the Navier-Stokes equations , 1985 .

[3]  J. N. Reddy,et al.  On penalty function methods in the finite‐element analysis of flow problems , 1982 .

[4]  Wing Kam Liu,et al.  Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation , 1979 .

[5]  J. Tinsley Oden,et al.  Finite Elements: Fluid Mechanics. , 1989 .

[6]  Carlos A. Felippa,et al.  Iterative procedures for improving penalty function solutions of algebraic systems , 1978 .

[7]  L. Herrmann.  Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem , 1965 .

[8]  J. P. Benque,et al.  A finite element method for Navier-Stokes equations , 1980 .

[9]  R. Temam.  Navier-Stokes Equations , 1977 .

[10]  Graham F. Carey,et al.  Penalty finite element method for the Navier-Stokes equations , 1984 .

[11]  D. Malkus.  Eigenproblems associated with the discrete LBB condition for incompressible finite elements , 1981 .

[12]  R. S. Marshall,et al.  Viscous incompressible flow by a penalty function finite element method , 1981 .

[13]  A. Baker.  On a penalty finite element CFD algorithm for high speed flow , 1985 .

[14]  Ramon Codina,et al.  An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations , 1993 .

[15]  D. Malkus,et al.  Mixed finite element methods—reduced and selective integration techniques: a unification of concepts , 1990 .

[16]  J. Heinrich,et al.  Finite elements simulation of buoyancy-driven flows with emphasis on natural convection in a horizontal circular cylinder , 1988 .

[17]  Miguel Cervera,et al.  A PENALTY FINITE ELEMENT METHOD FOR NON-NEWTONIAN CREEPING FLOWS , 1993 .

[18]  J. Heinrich,et al.  A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows , 1990 .

[19]  O. C. Zienkiewicz,et al.  A penalty function approach to problems of plastic flow of metals with large surface deformations , 1975 .

[20]  R. Taylor,et al.  High Reynolds number, steady, incompressible flows by a finite element method. , 1976 .

[21]  Penalty solution of the Navier-Stokes equations , 1987 .

[22]  J. Tinsley Oden,et al.  PENALTY-FINITE ELEMENT METHODS FOR THE ANALYSIS OF STOKESIAN FLOWS* , 1982 .

[23]  J. N. Reddy,et al.  A penalty finite element model for axisymmetric flows of non‐Newtonian fluids , 1988 .

[24]  J. Heinrich,et al.  Physically correct penalty‐like formulations for accurate pressure calculation in finite element algorithms of the Navier‐Stokes equations , 1993 .

[25]  Robert L. Spilker,et al.  A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues , 1990 .

[26]  J. Heinrich,et al.  An application of small-gap equations in sealing devices , 1993 .

[27]  J. Heinrich.  A finite element model for double diffusive convection , 1984 .

[28]  O. C. Zienkiewicz,et al.  Constrained variational principles and penalty function methods in finite element analysis , 1974 .

[29]  Robert L. Lee,et al.  Smoothing techniques for certain primitive variable solutions of the Navier–Stokes equations , 1979 .

[30]  J. D. Ramshaw,et al.  A hybrid penalty—pseudocompressibility method for transient incompressible fluid flow , 1991 .

[31]  O. Zienkiewicz,et al.  Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables , 1978 .

[32]  R. A. Silverman,et al.  The Mathematical Theory of Viscous Incompressible Flow , 1972 .

[33]  O. C. Zienkiewicz,et al.  ITERATIVE METHOD FOR CONSTRAINED AND MIXED APPROXIMATION. AN INEXPENSIVE IMPROVEMENT OF F.E.M. PERFORMANCE , 1985 .

[34]  J. Reddy,et al.  A Comparison of a Penalty Finite Element Model with the Stream Function-Vorticity Model of Natural Convection in Enclosures , 1980 .

[35]  I. Babuska.  The Finite Element Method with Penalty , 1973 .

[36]  R. L. Sani,et al.  Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements , 1982 .

[37]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[38]  E. T. Olsen,et al.  Obtaining error estimates for optimally constrained incompressible finite elements , 1984 .

[39]  E.-M. Salonen,et al.  An iterative penalty function method in structural analysis , 1976 .

[40]  M. Bercovier,et al.  A finite element for the numerical solution of viscous incompressible flows , 1979 .

[41]  B. Simon,et al.  Multiphase Poroelastic Finite Element Models for Soft Tissue Structures , 1992 .

[42]  R. Courant.  Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[43]  J. Heinrich,et al.  Mesh generation and flow calculations in highly contorted geometries , 1996 .

[44]  Juan C. Heinrich,et al.  Petrov-Galerkin methods for the time-dependent convective transport equation , 1986 .

[45]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[46]  Graham F. Carey,et al.  Penalty approximation of stokes flow , 1982 .

[47]  川口 光年,et al.  O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円. , 1964 .

[48]  Graham F. Carey,et al.  Convergence of iterative methods in penalty finite element approximation of the Navier-Stokes equations , 1987 .

[49]  J. T. Oden,et al.  RIP-methods for Stokesian flows. , 1982 .