6 papers
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…
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.…
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro +1
This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equat…
The eXtended Virtual Element Method for elliptic problems with weakly singular solutions
Jerome Droniou, Gianmarco Manzini, Liam Yemm
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment…
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…
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…