Numerical Variational Methods Applied to Cylinder Buckling

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal with a one-dimensional null space. We show that we can construct many different solutions from a complex energy surface. We examine numerically convergence in the spatial discretization and in the domain size. Finally we give a physical interpretation of some of the solutions found. Key words. mountain-pass algorithm, steepest descent, continuation AMS subject classifications. 65Z05, 65N06, 65K10, 35J35, 35J60 DOI. 10.1137/060675241

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Jirí Horák, Gabriel J. Lord, Mark A. Peletier
• Keywords: Complex Energy Surface, Computational Variational Methods, One-dimensional Null Space, SIAMSC 2008