372 citations · 905 across the 41 of their papers we have counts for
49 papers
Numerical simulation of biological capsules based on interface-fitted polygonal meshes
Daniele A. Di Pietro, Simon Mendez, Aurelio E. Spadotto
In this work we introduce a numerical framework for the simulation of biological capsules based on meshes that adapt iteration-wise to the shape of the membrane. The discretization…
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…
poly_rust: a domain-specific language for polytopal methods with a Rust interpreter
Daniele A. Di Pietro
Background: Over the last two decades, considerable effort in the applied mathematics community has been devoted to the development of polytopal methods, i.e., numerical methods fo…
Optimal -error estimates and -multigrid convergence for Hybrid High-Order discretizations of the Poisson equation
Daniele A. Di Pietro, Emil Hössjer
This paper presents two new theoretical results for Hybrid High-Order (HHO) methods applied to elliptic problems. First, we establish -error estimates for the HHO discretizatio…
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…
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…
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 Reynolds-semi-robust H(div)-conforming method for unsteady incompressible power-law flows
Lourenço Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile
In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressib…
Serendipity discrete complexes with enhanced regularity
Daniele Di Pietro, Marien Hanot, Marwa Salah
In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of…
Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure
Lorenzo Botti, Michele Botti, Daniele Antonio Di Pietro +1
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusi…
Homogeneous multigrid for hybrid discretizations: application to HHO methods
Daniele A. Di Pietro, Zhaonan Dong, Guido Kanschat +2
We prove the uniform convergence of the geometric multigrid V-cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously establis…
A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection
Lourenço Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile
We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and -type diffusion, with Sobolev indices . The discretization of the d…
A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations
Daniele A. Di Pietro, Jerome Droniou, Jia Jia Qian
In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a red…
An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact
Ilaria Fontana, Daniele A. Di Pietro
We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this probl…
Uniform Poincaré inequalities for the Discrete de Rham complex on general domains
Daniele A. Di Pietro, Marien-Lorenzo Hanot
In this paper we prove Poincaré inequalities for the Discrete de Rham (DDR) sequence on a general connected polyhedral domain of . We unify the ideas behind the i…
A discrete three-dimensional divdiv complex on polyhedral meshes with application to a mixed formulation of the biharmonic problem
Daniele A. Di Pietro, Marien-Lorenzo Hanot
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discre…
An exterior calculus framework for polytopal methods
Francesco Bonaldi, Daniele A. Di Pietro, Jerome Droniou +1
We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete vers…
A polytopal method for the Brinkman problem robust in all regimes
Daniele A. Di Pietro, Jérôme Droniou
In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meani…
Cohomology of the discrete de Rham complex on domains of general topology
Daniele A. Di Pietro, Jérôme Droniou, Silvano Pitassi
In this work we prove that, for a general polyhedral domain of , the cohomology spaces of the discrete de Rham complex of [Di Pietro and Droniou, An arbitrary-order d…
A serendipity fully discrete div-div complex on polygonal meshes
Michele Botti, Daniele A. Di Pietro, Marwa Salah
In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version…
Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
Daniele A. Di Pietro, Jérôme Droniou
In this work we investigate from a broad perspective the reduction of degrees of freedom through serendipity techniques for polytopal methods compatible with Hilbert complexes. We…
A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem
Daniele A. Di Pietro, Jérôme Droniou
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation o…
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro +1
This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equat…
A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes
Daniele A. Di Pietro, Jerome Droniou
In this work we propose a discretisation method for the Reissner--Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order. T…