CONVERGENT FINITE-ELEMENTS FOR A CLASS OF NONCONVEX VARIATIONAL-PROBLEMS

We study the finite element discretization of the abstract minimizatio n problem min{F(u)}. The functional F is neither convex nor growing at co. For the admissible class C-M = {u : Omega --> R, u concave, 0 les s than or equal to u(x) less than or equal to M} polygonal domains Ome ga subset of R-2 and linear Courant triangles, we show the convergence of the finite element approximations to a minimizer of F(u). A class of projected Newton methods for the discrete problems yields locally s uperlinear convergence. We present numerical experiments for a model f unctional F, related to Newton's problem of minimal resistance of a bo dy moving through a fluid.