88 citations · 175 across the 24 of their papers we have counts for
5 papers · 1 filter
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…