7 papers · 1 filter
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…
A Staggered Discontinuous Galerkin Method for linear elasticity problem on Polytopal Meshes
Long Chen, Xuehai Huang, Ruishu Wang +1
This paper develops a novel staggered discontinuous Galerkin (SDG) method for linear elasticity based on the Hellinger-Reissner variational principle. We construct symmetric stress…
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…
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…
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…