13 papers
An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency
Daniele Antonio Di Pietro, Jérôme Droniou
In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An arbitrar…
Non-conforming finite elements on polytopal meshes
Jerome Droniou, Robert Eymard, Thierry Gallouet +1
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first prese…
An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
Daniele A. Di Pietro, Jérôme Droniou
In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a…
Hessian discretisation method for fourth order semi-linear elliptic equations: applications to the von Kármán and Navier--Stokes models
Jérome Droniou, Neela Nataraj, Devika Shylaja
This paper deals with the Hessian discretisation method (HDM) for fourth order semi-linear elliptic equations with a trilinear nonlinearity. The HDM provides a generic framework fo…
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray-Lions operator
Jerome Droniou, Beniamin Goldys, Kim-Ngan Le
*The gradient discretisation method (GDM) is a generic framework, covering many classical methods (Finite Elements, Finite Volumes, Discontinuous Galerkin, etc.), for designing and…
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
Jerome Droniou, Robert Eymard
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and no…