Bregman divergences and error control via convex duality

• Date: 19. 3. 2026
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K1
• Speaker: Alexei Gazca

Convex duality relations are a useful tool for deriving error estimates for challenging nonlinear and non-smooth variational problems, including total variation minimisation, the p-Laplacian, the obstacle problem, elastoplastic torsion, among others. Applied at the continuous level they can deliver nonlinear analogues of the Prager-Synge a posteriori error identity, while at the discrete level they allow the derivation of minimal regularity a priori estimates. By leveraging elementary properties of Bregman divergences, we obtain three results on the error control via convex duality for a general class of problems: first, we prove the local efficiency of the duality gap error estimator, secondly, we derive a guaranteed a posteriori bound for non-conforming fields, and finally, we prove a minimal-regularity quasioptimal estimate for a Crouzeix--Raviart discretisation of the (phi)-Laplace problem. We will also discuss extensions to the vectorial setting, focusing on the prototypical incompressible Stokes and linear elasticity systems. This is joint work with Alex Kaltenbach (TU Berlin).