88 citations · 175 across the 24 of their papers we have counts for
24 papers
A family of mixed-mixed strongly conservative finite element methods for Biot's model of consolidation
Qingguo Hong, Johannes Kraus, Maria Lymbery
We consider a four-field formulation of Biot's quasi-static model of consolidation with the (effective) elastic stress, the solid displacement, the fluid flux and the fluid pressur…
A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems
Fei Li, Qingguo Hong, Ming Tang +1
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the…
Greedy Algorithm for Neural Networks for Indefinite Elliptic Problems
Qingguo Hong, Jiwei Jia, Young Ju Lee +1
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of th…
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration
Qijia Zhai, Qingguo Hong, Xiaoping Xie
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet bo…
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Qingguo Hong, Jonathan W. Siegel, Qinyang Tan +1
Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of vie…
A sharp Korn's inequality for piecewise space and its application
Qingguo Hong, YounJu Lee, Jinchao Xu
In this paper, we revisit Korn's inequality for the piecewise space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed…
An efficient iterative method for dynamical Ginzburg-Landau equations
Qingguo Hong, Limin Ma, Jinchao Xu
In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner fo…
Generalized Korn's Inequalities for Piecewise Vector Fields
David M. Williams, Qingguo Hong
The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's in…
Robust approximation of generalized Biot-Brinkman problems
Q. Hong, J. Kraus, M. Kuchta +3
The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study c…
Greedy Training Algorithms for Neural Networks and Applications to PDEs
Jonathan W. Siegel, Qingguo Hong, Xianlin Jin +2
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engi…
A Priori Analysis of Stable Neural Network Solutions to Numerical PDEs
Qingguo Hong, Jonathan W. Siegel, Jinchao Xu
Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K…
A new practical framework for the stability analysis of perturbed saddle-point problems and applications
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babuska…
An Extended Galerkin analysis in finite element exterior calculus
Qingguo Hong, Yuwen Li, Jinchao Xu
For the Hodge--Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contrac…
An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
Qingguo Hong, Chunmei Liu, Jinchao Xu
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract sta…
New Discontinuous Galerkin Algorithms and Analysis for Linear Elasticity with Symmetric Stress Tensor
Qingguo Hong, Jun Hu, Limin Ma +1
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The an…
Robust block preconditioners for poroelasticity
Shuangshuang Chen, Qingguo Hong, Jinchao Xu +1
In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several precondit…
Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot's consolidation and multiple-network poroelasticity models
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
This work is concerned with the iterative solution of systems of quasi-static multiple-network poroelasticity (MPET) equations describing flow in elastic porous media that is perme…
An Extended Galerkin Analysis for Elliptic Problems
Qingguo Hong, Shuonan Wu, Jinchao Xu
A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For second order elli…
Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also refe…
Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memory
Wansheng Wang, Qingguo Hong
In this paper, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algori…
Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
Qingguo Hong, Jinchao Xu
In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standa…
A Unified Study of Continuous and Discontinuous Galerkin Methods
Qingguo Hong, Fei Wang, Shuonan Wu +1
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid F…
Parameter-robust stability of classical three-field formulation of Biot's consolidation model
Qingguo Hong, Johannes Kraus
This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (…