9 citations · 9 across the 4 of their papers we have counts for
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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…
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…