372 citations · 1.4k across the 57 of their papers we have counts for
9 papers · 2 filters
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…