Get access
Advertisement

A family of residual-based stabilized finite element methods for Stokes flows

Authors

  • Eugenio Oñate,

    Corresponding author
    1. International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Campus Norte UPC, 08034 Barcelona, Spain
    • CIMNE, Edificio C1, Campus Norte, UPC, Gran Capitán s/n, 08034 Barcelona, Spain
    Search for more papers by this author
  • Prashanth Nadukandi,

    1. International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Campus Norte UPC, 08034 Barcelona, Spain
    Search for more papers by this author
  • Sergio R. Idelsohn,

    1. International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Campus Norte UPC, 08034 Barcelona, Spain
    Search for more papers by this author
    • ICREA Research Professor at CIMNE.

  • Julio García,

    1. International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Campus Norte UPC, 08034 Barcelona, Spain
    Search for more papers by this author
  • Carlos Felippa

    1. Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado, Boulder, CO 80309-0429, U.S.A.
    Search for more papers by this author
    • Visiting Professor at CIMNE.


Abstract

We present a collection of stabilized finite element (FE) methods derived via first- and second-order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub-scales (OSS) method are recovered from the general residual-based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual-based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented. Copyright © 2010 John Wiley & Sons, Ltd.

Get access to the full text of this article

Ancillary