On two matrix-free continuation approaches for the determination of the bifurcation diagram of the von Kármán system

In this paper we present a combination of the asymptotic numerical continuation procedure with a preconditioned GMRES-solver as applied to the fourth-order non linear von Kármán problem. Using a mixed equal order finite element discretization, we show how our “matrix free”approach allows for an efficient determination of the non-trivial branch of the bifurcation diagram. We also show that, using a steplength estimation of Gervais and Sadiky [GER 04], one can limit himself to a third order prediction without loosing too much in the number of continuation steps.