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6 papers · 1 filter
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…
Enriching continuous Lagrange finite element approximation spaces using neural networks
Hélène Barucq, Michel Duprez, Florian Faucher +5
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural netw…
A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes
Daniel Castanon Quiroz, Daniele A. Di Pietro
In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial…
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…
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…
Analysis of BDDC preconditioners for non-conforming polytopal hybrid discretisation methods
Santiago Badia, Jerome Droniou, Jordi Manyer +1
In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; \href{https://doi.org/10.1007…