On penalty function methods in the finiteelement analysis of flow problems
Abstract
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 NavierStokes equations. Conditions for the equivalence of two penaltyfinite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 June 1982
 DOI:
 10.1002/fld.1650020204
 Bibcode:
 1982IJNMF...2..151R
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Penalty Function;
 Stokes Flow;
 Boundary Value Problems;
 Convective Flow;
 Convergence;
 Flow Equations;
 Flow Velocity;
 Fluid Flow;
 Incompressible Flow;
 NavierStokes Equation;
 Optimization;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer