Nonconforming discretizations of convex minimization problems and precise relations to mixed methods

This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of nonconformity errors. A reconstruction formula provides the discrete solution problem via a postprocessing procedure which implies strong duality relation is interest in posteriori estimation. The framework applies differentiable nonsmooth problems, examples include p -Laplace, total-variation regularized, obstacle problems. Numerical experiments illustrate advantages over standard conforming methods.