Explicit and efficient error estimation for convex minimization problems

Sören Bartels; Alex Kaltenbach

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arXiv · 2204.10745

Explicit and efficient error estimation for convex minimization problems

Sören Bartels·Alex Kaltenbach

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Abstract

We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The 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. In addition, these a posteriori error estimates are based on a comparison to a given non-conforming finite element solution. For the $p$-Dirichlet problem, these a posteriori error bounds are equivalent to residual type a posteriori error bounds and, hence, reliable and efficient.

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Sören Bartels, Alex Kaltenbach. 2022-04-22. Explicit and efficient error estimation for convex minimization problems. https://arxiv.org/abs/2204.10745

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