Convergent adaptive hybrid higher-order schemes for convex minimization

@article{Carstensen2022ConvergentAH,
title={Convergent adaptive hybrid higher-order schemes for convex minimization},
author={Carsten Carstensen and Ngoc Tien Tran},
journal={ArXiv},
year={2022},
volume={abs/2111.01181}
}
• Published 1 November 2021
• Mathematics
• ArXiv
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology optimization, and the convexified double-well problem. The hybrid high-order method utilizes a gradient reconstruction in the space of piecewise Raviart–Thomas finite element functions without stabilization on triangulations into simplices or in the space of piecewise…

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