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