5 papers · 1 filter
A Reynolds- and Hartmann-semirobust hybrid method for magnetohydrodynamics
Daniele A. Di Pietro, Jerome Droniou, Vito Patierno
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-val…
A low-order hybrid method for the variable-density incompressible Navier-Stokes equations
Mathias Dauphin, Daniele A. Di Pietro, Jérôme Droniou +1
In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the su…
Conforming lifting and adjoint consistency for the Discrete de Rham complex of differential forms
Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi
Discrete de Rham (DDR) methods provide non-conforming but compatible approximations of the continuous de Rham complex on general polytopal meshes. Owing to the non-conformity, seve…
From Finite Elements to Hybrid High-Order methods
Daniele A. Di Pietro, Jérôme Droniou
This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an over…
A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations
Lourenço Beirão da Veiga, Daniele A. Di Pietro, Jérôme Droniou +2
In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discre…