3 citations · 3 across the 9 of their papers we have counts for
11 papers
Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff--Love plates
Daniele A. Di Pietro, Jérôme Droniou, Kaibo Hu +1
We develop and analyse a new arbitrary-order method for the Kirchhoff--Love plate problem on general polygonal meshes. The construction relies on a discrete Hessian complex obtaine…
Key challenges and bridges among convergence analysis techniques for polytopal methods
Lourenço Beirão da Veiga, Daniele Antonio Di Pietro, Jérôme Droniou
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific chall…
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…
Ghost stabilisation for cut finite element exterior calculus
Daniele Di Pietro, Jérôme Droniou, Erik Nilsson
We introduce the cut finite element method in the language of finite element exterior calculus, by formulating a stabilisation -- for any form degree -- that makes the method robus…
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…
Design and homological analysis of twisted and BGG Stokes-de Rham complexes on polygonal meshes
Daniele A. Di Pietro, Jérôme Droniou, Kaibo Hu +1
We design a discrete Bernstein--Gelfand--Gelfand (BGG) diagram in a two-dimensional setting on polygonal meshes based on the DDR framework; the diagram is made of a discrete Stokes…
A Hybrid High-Order method for the power-law Brinkman problem with robust error estimates in all regimes
Daniel Castañón Quiroz, Daniele A. Di Pietro, Jérôme Droniou +1
In this work we propose and analyze a new Hybrid High-Order method for the Brinkman problem for fluids with power-law viscosity. The proposed method supports general meshes and arb…
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…
A mixed finite element method for a sixth order elliptic problem
Jérôme Droniou, Muhammad Ilyas, Bishnu Lamichhane +1
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciar…