Local discontinuous Galerkin FEM for convex minimization

arXiv:2604.08246v3 Announce Type: replace Abstract: The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discretizations for p-Laplace type minimization problems provide upper bounds of the energy difference with optimal convergence rates. Even for smooth solutions, known convergence rates for higher-order non-conforming finite element discretizations for the same problem class with $2