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math.NA2025
Finite element conformal complexes in three dimensions
Xuehai Huang
This paper extends the Bernstein-Gelfand-Gelfand (BGG) framework to the construction of finite element conformal Hessian complexes and conformal elasticity complexes in three dimen…
math.NA2025
An Optimal and Robust Nonconforming Finite Element Method for the Strain Gradient Elasticity
Jianguo Huang, Xuehai Huang, Zheqian Tang
An optimal and robust low-order nonconforming finite element method is developed for the strain gradient elasticity (SGE) model in arbitrary dimensions. An -nonconforming quad…
math.NA2025
Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem
Xuehai Huang, Zheqian Tang
A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed…