Continuation techniques for a penalty approximation of the Navier-Stokes equations

Abstract

Continuation techniques are used to solve a penalty finite element approximation of the Navier-Stokes equations. Sufficient conditions are given for convergence of the Euler-Newton 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.