10 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…
poly_rust: a domain-specific language for polytopal methods with a Rust interpreter
Daniele A. Di Pietro
In this article we introduce poly_rust, a new software library that implements a domain-specific language for polytopal methods. Polytopal methods support meshes much more general…
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…