14 papers
Representation Theorems for Actual Powers over Two-Agent General Concurrent Game Frames
Zixuan Chen, Fengkui Ju, Thomas Ågotnes
One of the most well-known connections between logic and games is Pauly's representation theorem: the induced powers of individuals and coalitions in concurrent game frames corresp…
Low-regularity finite element elasticity complexes with hybridizable stresses on tetrahedral Alfeld splits
Johnny Guzmán, Xuehai Huang
Finite element elasticity complexes of low regularity are constructed on tetrahedral Alfeld splits. In comparison with existing three-dimensional elasticity complexes on such split…
Hybridizable Staggered Discontinuous Galerkin Methods for Polyharmonic Equations on Polytopes
Long Chen, Xuehai Huang, Yule Sun +1
Hybridizable staggered discontinuous Galerkin methods are developed for arbitrary-order polyharmonic equations on shape-regular polytopal meshes in , for…
Explicit Planar Finite Element Elasticity Complexes and Elements on Barycentric Refinements
Chunyu Chen, Long Chen, Xuehai Huang
The exact-sequence structure behind the Arnold--Douglas--Gupta family of higher-order mixed finite elements for plane elasticity on barycentric refinements is made explicit. On eac…
Nonconforming Linear Element Method for a Generalized Tensor-Valued Stokes Equation with Application to the Triharmonic Equation
Ziwen Gu, Xuehai Huang
A nonconforming linear element method is developed for a three-dimensional generalized tensor-valued Stokes equation associated with the Hessian complex in this paper. A discrete H…
Superconvergent and Divergence-Free Mixed Finite Element Methods for The Stokes Equation
Long Chen, Xuehai Huang, Chao Zhang +1
This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup conditi…
Implementation and Basis Construction for Smooth Finite Element Spaces
Chunyu Chen, Long Chen, Tingyi Gao +2
The construction of conforming finite elements on simplicial meshes has recently advanced through the groundbreaking work of Hu, Lin, and Wu (Found. Comput. Math. 24, 2024).…
Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
Xuewei Cui, Xuehai Huang
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the space in three dimensions is proposed, involving an -nonconforming…
Hybridizable Symmetric Stress Elements on the Barycentric Refinement in Arbitrary Dimensions
Long Chen, Xuehai Huang
Hybridizable \(H(\textrm{div})\)-conforming finite elements for symmetric tensors on simplices with barycentric refinement are developed in this work for arbitrary dimensions and a…
A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes
L. Chen, X. Huang, E. Park +1
This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid fr…
Tangential-Normal Decompositions of the Second Family of Finite Element Differential Forms
Long Chen, Xuehai Huang
This paper introduces a novel tangential-normal (-) decomposition for the second family of finite element differential forms, presenting a new framework for constructing base…
Decoupled finite element methods for a fourth-order exterior differential equation
Xuewei Cui, Xuehai Huang
This paper proposes novel decoupled finite element methods for a fourth-order exterior differential equation. Based on differential complexes and the Helmholtz decomposition, the f…
Distributional Finite Element curl div Complexes and Application to Quad Curl Problems
Long Chen, Xuehai Huang, Chao Zhang
The paper addresses the challenge of constructing finite element curl div complexes in three dimensions. Tangential-normal continuity is introduced in order to develop distribution…
New low-order mixed finite element methods for linear elasticity
Xuehai Huang, Chao Zhang, Yaqian Zhou +1
New low-order -conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the sy…