6 citations · 7 across the 9 of their papers we have counts for
9 papers
Cohomology of Finite Element Stokes Complexes on Alfeld Splits
Pablo D. Brubeck, Yizhou Liang, Charles Parker
We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzmán, & Neilan (2020, Math. Comp., 89…
Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
Jun Hu, Yizhou Liang, Ting Lin
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite ele…
Local Bounded Commuting Projection Operators for Discrete Gradgrad Complexes
Jun Hu, Yizhou Liang, Ting Lin
This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an importan…
Local Bounded Commuting Projection Operator for Discrete de Rham Complexes
Jun Hu, Yizhou Liang, Ting Lin
The local bounded commuting projection operators of nonstandard finite element de Rham complexes in two and three dimensions are constructed systematically. The assumptions of the…
Finite element grad grad complexes and elasticity complexes on cuboid meshes
Jun Hu, Yizhou Liang, Ting Lin
This paper constructs two conforming finite element grad grad and elasticity complexes on the cuboid meshes. For the finite element grad grad complex, an conforming finite el…
New conforming finite element divdiv complexes in three dimensions
Jun Hu, Yizhou Liang, Rui Ma +1
In this paper, the first family of conforming finite element divdiv complexes on cuboid grids in three dimensions is constructed. Besides, a new family of conforming finite element…
Conforming finite element DIVDIV complexes and the application for the linearized Einstein-Bianchi system
Jun Hu, Yizhou Liang, Rui Ma
This paper presents the first family of conforming finite element divdiv complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\text{d…
Some Computations on Instanton Knot Homology
Zhenkun Li, Yi Liang
In a recent paper, the first author and his collaborator developed a method to compute an upper bound of the dimension of instanton Floer homology via Heegaard Diagrams of 3-manifo…
Conforming Discrete Gradgrad-Complexes in Three Dimensions
Jun Hu, Yizhou Liang
In this paper, the first family of conforming discrete three dimensional Gradgrad-complexes consisting of finite element spaces is constructed. These discrete complexes are exact i…