Functional analysis and exterior calculus on mixed-dimensional geometries
We are interested in differential forms on mixed-dimensional geometries, in the sense of a
domain containing sets of d-dimensional manifolds, structured hierarchically so that each d …
domain containing sets of d-dimensional manifolds, structured hierarchically so that each d …
Smoothed projections and mixed boundary conditions
M Licht - Mathematics of Computation, 2019 - ams.org
Mixed boundary conditions are introduced to finite element exterior calculus. We construct
smoothed projections from Sobolev de Rham complexes onto finite element de Rham …
smoothed projections from Sobolev de Rham complexes onto finite element de Rham …
An exterior calculus framework for polytopal methods
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 versions …
inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions …
Abstractions and automated algorithms for mixed domain finite element methods
C Daversin-Catty, CN Richardson… - ACM Transactions on …, 2021 - dl.acm.org
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown
fields defined over domains of differing topological dimension. Such equations naturally …
fields defined over domains of differing topological dimension. Such equations naturally …
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces
spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh …
spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh …
Local finite element approximation of Sobolev differential forms
We address fundamental aspects in the approximation theory of vector-valued finite element
methods, using finite element exterior calculus as a unifying framework. We generalize the …
methods, using finite element exterior calculus as a unifying framework. We generalize the …
A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes
WM Boon, A Fumagalli - Journal of Scientific Computing, 2023 - Springer
A solution technique is proposed for flows in porous media that guarantees local
conservation of mass. We first compute a flux field to balance the mass source and then …
conservation of mass. We first compute a flux field to balance the mass source and then …
Distributional Hessian and divdiv complexes on triangulation and cohomology
In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG)
complexes, ie, the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The …
complexes, ie, the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The …
discrete de-Rham complex involving a discontinuous finite element space for velocities: the case of periodic straight triangular and Cartesian meshes
V Perrier - arXiv preprint arXiv:2404.19545, 2024 - arxiv.org
The aim of this article is to derive discontinuous finite elements vector spaces which can be
put in a discrete de-Rham complex for which an harmonic gap property may be proven. First …
put in a discrete de-Rham complex for which an harmonic gap property may be proven. First …
Smoothed projections over manifolds in finite element exterior calculus
MW Licht - arXiv preprint arXiv:2310.14276, 2023 - arxiv.org
We develop commuting finite element projections over smooth Riemannian manifolds. This
extension of finite element exterior calculus establishes the stability and convergence of …
extension of finite element exterior calculus establishes the stability and convergence of …