On penalty function methods in the finite‐element analysis of flow problems Academic Article uri icon


  • In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier‐Stokes equations. Conditions for the equivalence of two penalty‐finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem. Copyright © 1982 John Wiley & Sons, Ltd

author list (cited authors)

  • Reddy, J. N.

citation count

  • 113

publication date

  • April 1982