372 citations · 1.4k across the 57 of their papers we have counts for
67 papers
The eXtended Virtual Element Method for elliptic problems with weakly singular solutions
Jerome Droniou, Gianmarco Manzini, Liam Yemm
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment…
A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations
Daniele A. Di Pietro, Jerome Droniou, Jia Jia Qian
In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a red…
Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity
J Droniou, R Eymard, T Gallouët +2
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler…
Numerical analysis of the stochastic Stefan problem
Jerome Droniou, Muhammad Awais Khan, Kim Ngan Le
The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise.…
Two arbitrary-order constraint-preserving schemes for the Yang--Mills equations on polyhedral meshes
Jérôme Droniou, Jia Jia Qian
Two numerical schemes are proposed and investigated for the Yang--Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-value…
An exterior calculus framework for polytopal methods
Francesco Bonaldi, Daniele A. Di Pietro, Jerome Droniou +1
We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete vers…
A polytopal method for the Brinkman problem robust in all regimes
Daniele A. Di Pietro, Jérôme Droniou
In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meani…
Cohomology of the discrete de Rham complex on domains of general topology
Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi
In this work we prove that, for a general polyhedral domain of , the cohomology spaces of the discrete de Rham complex of [Di Pietro and Droniou, An arbitrary-order d…
A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations
Jérôme Droniou, Todd A. Oliynyk, Jia Jia Qian
We present a discretisation of the 3+1 formulation of the Yang-Mills equations in the temporal gauge, using a Lie algebra-valued extension of the discrete de Rham (DDR) sequence, t…
Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
Daniele A. Di Pietro, Jérôme Droniou
In this work we investigate from a broad perspective the reduction of degrees of freedom through serendipity techniques for polytopal methods compatible with Hilbert complexes. We…
A hybrid high-order scheme for the stationary, incompressible magnetohydrodynamics equations
Jérôme Droniou, Liam Yemm
We propose and analyse a hybrid high-order (HHO) scheme for stationary incompressible magnetohydrodynamics equations. The scheme has an arbitrary order of accuracy and is applicabl…
Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
Francesco Bonaldi, Jérôme Droniou, Roland Masson
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including fric…
A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem
Daniele A. Di Pietro, Jérôme Droniou
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation o…
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro +1
This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equat…
A cost-effective nonlinear extremum-preserving finite volume scheme for highly anisotropic diffusion on Cartesian grids, with application to radiation belt dynamics
Nour Dahmen, Jerome Droniou, Francois Rogier
We construct a new nonlinear finite volume (FV) scheme for highly anisotropic diffusion equations, that satisfies the discrete minimum-maximum principle. The construction relies on…
Conditioning of a Hybrid High-Order scheme on meshes with small faces
Santiago Badia, Jerome Droniou, Liam Yemm
We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the Poisson problem. We find the condition number of the statically condensed system to be independen…
Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix-fracture interfaces
Francesco Bonaldi, Jérôme Droniou, Roland Masson +1
We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix-fracture interfaces. Fractures a…
A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes
Daniele A. Di Pietro, Jerome Droniou
In this work we propose a discretisation method for the Reissner--Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order. T…
An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency
Daniele Antonio Di Pietro, Jérôme Droniou
In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An arbitrar…
Robust Hybrid High-Order method on polytopal meshes with small faces
Jerome Droniou, Liam Yemm
We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on th…
An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
Daniele Antonio Di Pietro, Jérôme Droniou
In this paper we present a novel arbitrary-order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into ranges of vector c…
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…