6 papers
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…
An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
Lorenzo Botti, Michele Botti, Daniele A. Di Pietro
In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the…