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  1. No Access

    Article

    Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons

    The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differ...

    Wenrui Hao, Qingguo Hong, **anlin ** in Journal of Scientific Computing (2024)

  2. No Access

    Article

    Robust Approximation of Generalized Biot-Brinkman Problems

    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 complex poromechanical interac...

    Qingguo Hong, Johannes Kraus, Miroslav Kuchta… in Journal of Scientific Computing (2022)

  3. No Access

    Article

    New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor

    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 analysis is based on a unified ...

    Qingguo Hong, Jun Hu, Limin Ma, **chao Xu in Numerische Mathematik (2021)

  4. No Access

    Article

    An extended Galerkin analysis for elliptic problems

    A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For the second-order elliptic equation −div(α∇u) = f,...

    Qingguo Hong, Shuonan Wu, **chao Xu in Science China Mathematics (2021)

  5. No Access

    Article

    A unified study of continuous and discontinuous Galerkin methods

    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 FEMs, discontinuous Galerkin (...

    Qingguo Hong, Fei Wang, Shuonan Wu, **chao Xu in Science China Mathematics (2019)

  6. No Access

    Article

    A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations

    We consider multigrid methods for discontinuous Galerkin \(H({\text {div}},\Omega )\) ...

    Qingguo Hong, Johannes Kraus, **chao Xu, Ludmil Zikatanov in Numerische Mathematik (2016)