8 citations · 10 across the 12 of their papers we have counts for
13 papers
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…
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…
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 …
Efficient iterative linearised solvers for numerical approximations of stochastic Stefan problems
Muhammad Awais Khan, Jérôme Droniou, Kim-Ngan Le +1
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the que…
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…
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…
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, Dro…
Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise
Jerome Droniou, Kim-Ngan Le, Jörn Wichmann
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-New…
A discrete trace theory for non-conforming polytopal hybrid discretisation methods
Santiago Badia, Jerome Droniou, Jai Tushar
In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defi…
Analysis of a VEM-fully discrete polytopal scheme with bubble stabilisation for contact mechanics with Tresca friction
Jérôme Droniou, Ali Haidar, Roland Masson
This work performs the convergence analysis of the polytopal nodal discretisation of contact-mechanics (with Tresca friction) recently introduced in [18] in the framework of poro-e…
Discretisations of mixed-dimensional Thermo-Hydro-Mechanical models preserving energy estimates
Jerome Droniou, Mohamed Laaziri, Roland Masson
In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM) models in fractured porous media accounting for Coulomb frictional contact at matrix fracture interfaces.…
A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations
Jérôme Droniou, Marien Hanot, Todd Oliynyk
We design in this work a discrete de Rham complex on manifolds. This complex, written in the framework of exterior calculus, has the same cohomology as the continuous de Rham compl…
A bubble VEM-fully discrete polytopal scheme for mixed-dimensional poromechanics with frictional contact at matrix fracture interfaces
Jérôme Droniou, Guillaume Enchéry, Isabelle Faille +2
The objective of this article is to address the discretisation of fractured/faulted poromechanical models using 3D polyhedral meshes in order to cope with the geometrical complexit…