Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

DOI10.1142/S0218202520500372zbMath1451.65173arXiv1911.03616OpenAlexW2986372024MaRDI QIDQ3386877

Francesca Rapetti, Jérôme Droniou, Daniele A. Di Pietro

Publication date: 7 January 2021

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.03616

zbMATH Keywords

mixed methodspolyhedral methodscompatible discretisationsfully discrete de Rham sequences

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for partial differential equations, boundary value problems (65N99) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (15)

An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence ⋮ A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem ⋮ Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes ⋮ Virtual elements for Maxwell's equations ⋮ A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics ⋮ An extended Galerkin analysis in finite element exterior calculus ⋮ Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method ⋮ An arbitrary-order fully discrete Stokes complex on general polyhedral meshes ⋮ A polytopal method for the Brinkman problem robust in all regimes ⋮ A pressure-robust discrete de Rham scheme for the Navier-Stokes equations ⋮ An arbitrary-order discrete de Rham complex on polyhedral meshes: exactness, Poincaré inequalities, and consistency ⋮ A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations ⋮ Cohomology of the discrete de Rham complex on domains of general topology ⋮ Exact sequences of conforming finite element spaces with interface constraints for macro polytopal meshes

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