Reliable and Efficient Approximation of Polyconvex Envelopes

An iterative algorithm that approximates the polyconvex envelope f pc of a given function f : R → R, i.e. the largest function below f which is convex in all minors, is established. A rigorous error analysis with a focus on reliability and optimal orders of convergence, an efficient strategy that reduces the large number of unknowns, as well as numerical experiments are presented.