372 citations · 1.4k across the 57 of their papers we have counts for
10 papers · 1 filter
Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems
Daniele Antonio Di Pietro, Jérôme Droniou, André Harnist
We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray-Lions problems set in W^(1,p) with p in (1,2]. Specifically, we prove that, depending on the de…
Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces
Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou +3
We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dim…
Non-conforming finite elements on polytopal meshes
Jerome Droniou, Robert Eymard, Thierry Gallouet +1
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first prese…
An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
Daniele A. Di Pietro, Jérôme Droniou
In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a…
Hessian discretisation method for fourth order semi-linear elliptic equations: applications to the von Kármán and Navier--Stokes models
Jérome Droniou, Neela Nataraj, Devika Shylaja
This paper deals with the Hessian discretisation method (HDM) for fourth order semi-linear elliptic equations with a trilinear nonlinearity. The HDM provides a generic framework fo…
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray-Lions operator
Jerome Droniou, Beniamin Goldys, Kim-Ngan Le
*The gradient discretisation method (GDM) is a generic framework, covering many classical methods (Finite Elements, Finite Volumes, Discontinuous Galerkin, etc.), for designing and…
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou +1
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfac…
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
Jerome Droniou, Robert Eymard
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and no…
Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes
Jerome Droniou
We explore the effects of mesh skewness on the accuracy of standard Hybrid High-Order (HHO) schemes for anisotropic diffusion equations. After defining a notion of regular skewed m…
Numerical solution of a two dimensional tumour growth model with moving boundary
Jerome Droniou, Jennifer A. Flegg, Gopikrishnan C. Remesan
We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A li…