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arXiv · 2606.21560

An Aubin-Nitsche Lemma for a positivity-preserving finite element method

Gabriel R. Barrenechea·Theophile Chaumont-Frelet
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Abstract

In this work we prove an Aubin-Nitsche Lemma for a positivity-preserving discretisation of an elliptic problem. Due to the nonlinearity of the discretisation, the result requires as a first step the proposal of a linearised adjoint problem that can be linked to the method of choice by appropriately selecting weights. This linearised adjoint problem, together with a regularity result, allow the proof of an optimal-order error estimate in the $L^2$-norm of the error.

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Gabriel R. Barrenechea, Theophile Chaumont-Frelet. 2026-06-19. An Aubin-Nitsche Lemma for a positivity-preserving finite element method. https://arxiv.org/abs/2606.21560

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