Alex Kaltenbach: A posteriori error estimation based on (discrete) convex duality relations
We combine a systematic approach for deriving general a posteriori
error estimates for convex minimization problems using convex duality relations with a recently derived generalized Marini formula. The resulting a posteriori error estimates are essentially constant-free and apply to a large class of variational problems including the p-Dirichlet problem, as well as degenerate minimization, obstacle and image de-noising problems.
For the p-Dirichlet problem, the a posteriori error bounds are equivalent to the classical residual type a posteriori error bounds and, hence, reliable and efficient.