17 citations · 61 across the 15 of their papers we have counts for
15 papers
A finite element algorithm for the sixth order problem with simply supported boundary conditions
Hengguang Li, Peimeng Yin
In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth…
A finite element method for the biharmonic problem with Dirichlet boundary conditions in a polygonal domain
Hengguang Li, Charuka D. Wickramasinghe, Peimeng Yin
In this paper, we study the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-o…
An adaptive finite element method for two-dimensional elliptic equations with line Dirac sources
Huihui Cao, Hengguang Li, Nianyu Yi +1
In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and gl…
Solving Biharmonic Eigenvalue Problem With Navier Boundary Condition Via Poisson Solvers On Non-Convex Domains
Baiju Zhang, Hengguang Li, Zhimin Zhang
It is well known that the usual mixed method for solving the biharmonic eigenvalue problem by decomposing the operator into two Laplacians may generate spurious eigenvalues on non-…
A finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
Hengguang Li, Peimeng Yin, Zhimin Zhang
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-ord…
Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources
Hengguang Li, Xiang Wan, Peimeng Yin +1
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measur…
A two-grid method for the interior penalty discretization of the Monge-Ampère equation
Gerard Awanou, Hengguang Li, Eric Malitz
The purpose of this paper is to analyze an efficient method for the solution of the nonlinear system resulting from the discretization of the elliptic Monge-Ampère equation by a $C…
A Novel Stochastic Stratified Average Gradient Method: Convergence Rate and Its Complexity
Aixiang Chen, Bingchuan Chen, Xiaolong Chai +2
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate a…
A new anisotropic finite element method on polyhedral domains: interpolation error analysis
Hengguang Li
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary,…
Regularity and a priori error analysis of a Ventcel problem in polyhedral domains
Serge Nicaise, Hengguang Li, Anna Mazzucato
We consider the regularity of a mixed boundary value problem for the Laplace operator on a polyhedral domain, where Ventcel boundary conditions are imposed on one face of the polyh…
Differential operators on domains with conical points: precise uniform regularity estimates
Constantin Bacuta, Hengguang Li, Victor Nistor
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses…
Uniform shift estimates for transmission problems and optimal rates of convergence for the parametric Finite Element Method
Hengguang Li, Victor Nistor, Yu Qiao
Let $Ω\subset \RR^d$, , be a bounded domain with piecewise smooth boundary and let be an open subset of a Banach space . Motivated by questions i…
Axisymmetric Stokes equations in polygonal domains: regularity and finite element approximations
Young Ju Lee, Hengguang Li
We study the regularity and finite element approximation of the axisymmetric Stokes problem on a polygonal domain . In particular, taking into account the singular coefficients…
Analysis of Schrödinger operators with inverse square potentials {II}: FEM and approximation of eigenfunctions in the periodic case
Eugenie Hunsicker, Hengguang Li, Victor Nistor +1
Let be a {\em periodic} potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form , with $ρ(x) = |…
Analysis of Schrödinger operators with inverse square potentials I: regularity results in 3D
Eugenie Hunsicker, Hengguang Li, Victor Nistor +1
Let be a potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form , with for …