Discrete weak duality of hybrid high-order methods for convex minimization problems
Numerical Analysis
2026-04-10 v3 Numerical Analysis
Abstract
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with convergence rates under additional smoothness assumptions. This duality holds for general polyhedral meshes and arbitrary polynomial degrees of the discretization. A novel postprocessing is proposed and allows for a~posteriori error estimates on regular triangulations into simplices using primal-dual techniques. This motivates an adaptive mesh-refining algorithm, which performs superiorly compared to uniform mesh refinements.
Cite
@article{arxiv.2308.03223,
title = {Discrete weak duality of hybrid high-order methods for convex minimization problems},
author = {Ngoc Tien Tran},
journal= {arXiv preprint arXiv:2308.03223},
year = {2026}
}