372 citations · 1.4k across the 57 of their papers we have counts for
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A discontinuous-skeletal method for advection-diffusion-reaction on general meshes
Daniele A. Di Pietro, Jérôme Droniou, Alexandre Ern
We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order at mesh faces.…
Finite volume schemes for diffusion equations: introduction to and review of modern methods
Jerome Droniou
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construc…
Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain
Michel Chipot, Jerome Droniou, Gabriela Planas +2
In this paper we treat three problems on a two-dimensional `punctured periodic domain': we take , where is the disc of radius centred at…
On a miscible displacement model in porous media flow with measure data
Jerome Droniou, Kyle S. Talbot
We establish the existence of a solution to a non-linearly coupled elliptic-parabolic system of PDEs describing the single-phase, miscible displacement of one incompressible fluid…
Gradient Schemes for Linear and Non-linear Elasticity Equations
Jerome Droniou, Bishnu P. Lamichhane
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient…