Continuation techniques for a penalty approximation of the NavierStokes equations
Abstract
Continuation techniques are used to solve a penalty finite element approximation of the NavierStokes equations. Sufficient conditions are given for convergence of the EulerNewton continuation method in a Reynolds parameter to an isolated solution of the finite element problem. Numerical results are presented for the 'driven cavity' problem. The approach is extended to arc length continuation to treat problems with singular points on the continuation path.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 April 1985
 DOI:
 10.1016/S00457825(85)800025
 Bibcode:
 1985CMAME..48..265C
 Keywords:

 Continuity (Mathematics);
 Finite Element Method;
 Incompressible Flow;
 NavierStokes Equation;
 Penalty Function;
 Steady Flow;
 Approximation;
 Boundary Value Problems;
 Computational Fluid Dynamics;
 Convergence;
 Euler Equations Of Motion;
 Existence Theorems;
 Newton Methods;
 Newton Theory;
 Reynolds Number;
 Variational Principles;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer