372 citations · 1.4k across the 57 of their papers we have counts for
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Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
Daniele A. Di Pietro, Jérôme Droniou, Francesca Rapetti
In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons a…
Convergence analysis of a numerical scheme for a tumour growth model
Jerome Droniou, Neela Nataraj, Gopikrishnan Chirappurathu Remesan
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumo…
An efficient implementation of mass conserving characteristic-based schemes in 2D and 3D
Hanz Martin Cheng, Jerome Droniou
In this paper, we develop the ball-approximated characteristics (B-char) method, which is an algorithm for efficiently implementing characteristic-based schemes in 2D and 3D. Core…
Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling
Jerome Droniou, Matej Medla, Karol Mikula
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discre…
The gradient discretisation method for linear advection problems
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equation…
High-order mass-lumped schemes for nonlinear degenerate elliptic equations
Jerome Droniou, Robert Eymard
We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piece…