10 papers
Error estimates for numerical approximations of a nonlinear gradient flow model
Jerome Droniou, Kim-Ngan Le, Huateng Zhu
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient d…
A higher order polytopal method for contact mechanics with Tresca friction
Jerome Droniou, Raman Kumar, Roland Masson +1
In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our ap…
A locking-free nodal-based polytopal method for linear elasticity
Jerome Droniou, Raman Kumar
This work presents a Discrete de Rham (DDR) numerical scheme for solving linear elasticity problems on general polyhedral meshes, with a focus on preventing volumetric locking in t…
Uniform Poincaré inequalities for the discrete de Rham complex of differential forms
Daniele Di Pietro, Jérôme Droniou, Marien-Lorenzo Hanot +1
In this paper we prove discrete Poincaré inequalities that are uniform in the mesh size for the discrete de Rham complex of differential forms developed in [Bonaldi, Di Pietro, Dr…
Analysis of BDDC preconditioners for non-conforming polytopal hybrid discretisation methods
Santiago Badia, Jerome Droniou, Jordi Manyer +1
In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; \href{https://doi.org/10.1007…
Commuting quasi-interpolators and Maxwell compactness for a polytopal de Rham complex
Théophile Chaumont-Frelet, Jérôme Droniou, Simon Lemaire
We establish Maxwell compactness results for the Discrete De Rham (DDR) polytopal complex: sequences in this polytopal complex with bounded discrete …