7 papers · 1 filter
A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes
Daniel Castanon Quiroz, Daniele A. Di Pietro
In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-…
An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem
Daniele A. Di Pietro
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construct…
A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method
Daniele Antonio Di Pietro, Ilaria Fontana, Kyrylo Kazymyrenko
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of…
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…
An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
Daniele Antonio Di Pietro, Jérôme Droniou
In this paper we present a novel arbitrary-order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into ranges of vector c…
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…