372 citations · 1.4k across the 57 of their papers we have counts for
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A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
Lorenzo Botti, Daniele Di Pietro, Jérôme Droniou
In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for…
A unified analysis of elliptic problems with various boundary conditions and their approximation
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue--Sobole…
A combined GDM--ELLAM--MMOC scheme for advection dominated PDEs
Hanz Martin Cheng, Jérôme Droniou, Kim-Ngan Le
We propose a combination of the Eulerian Lagrangian Localised Adjoint Method (ELLAM) and the Modified Method of Characteristics (MMOC) for time-dependent advection-domina\-ted PDEs…
A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation
Daniele A. Di Pietro, Jérôme Droniou
In this work, we present an abstract error analysis framework for the approximation of linear partial differential equation (PDE) problems in weak formulation. We consider approxim…
A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits
Lorenzo Botti, Daniele A. Di Pietro, Jérôme Droniou
In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements…
The Hessian discretisation method for fourth order linear elliptic equations
Jérôme Droniou, Bishnu P. Lamichhane, Devika Shylaja
In this paper, we propose a unified framework, the Hessian discretisation method (HDM), which is based on four discrete elements (called altogether a Hessian discretisation) and a…