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