Work

Singular solutions, graded meshes, and adaptivity for total-variation regularized minimization problems

Year: 2021

Type: preprint

Abstract: Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and devise numerical methods using locally refined meshes that lead to improved convergence rates despite the occurrence of discontinuities. It turns out that nearly linear convergence is possible on suitably constructed meshes.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2106.13561

Authors: Bartels, Sören, Tovey, Robert, Wassmer, Friedrich

Institution: University of Freiburg

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche

Awards: G188083318, G3010527862, Continous Image PRocESSIng: models and algorithms

OpenAlex ID: W4287113149

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