372 citations · 1.4k across the 57 of their papers we have counts for
6 papers · 1 filter
Numerical analysis of a two-phase flow discrete fracture model
Jerome Droniou, Julian Hennicker, Roland Masson
We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matr…
A gradient discretisation method to analyse numerical schemes for non-linear variational inequalities, application to the seepage problem
Yahya Alnashri, Jerome Droniou
Using the gradient discretisation method (GDM), we provide a complete and unified numerical analysis for non-linear variational inequalities (VIs) based on Leray--Lions operators a…
Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells
Jerome Droniou, Kyle S. Talbot
This article proves the existence of solutions to a model of incompressible miscible displacement through a porous medium, with zero molecular diffusion and modelling wells by spat…
The gradient discretisation method for optimal control problems, with super-convergence for non-conforming finite elements and mixed-hybrid mimetic finite differences
Jerome Droniou, Neela Nataraj, Devika Shylaja
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisat…
-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems
Daniele Di Pietro, Jerome Droniou
In this work we prove optimal -approximation estimates (with ) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupon…
Improved estimate for gradient schemes, and super-convergence of the TPFA finite volume scheme
Jerome Droniou, Neela Nataraj
The gradient discretisation method is a generic framework that is applicable to a number of schemes for diffusion equations, and provides in particular generic error estimates in $…