First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems. - Huangxin Chen; Guosheng Fu; Jingzhi Li 001; Weifeng Qiu (Comput. Math. Appl., 2014)

The Staggered DG Method is the Limit of a Hybridizable DG Method. - Eric T. Chung 001; Bernardo Cockburn; Guosheng Fu (SIAM J. Numer. Anal., 2014)

The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow. - Eric T. Chung 001; Bernardo Cockburn; Guosheng Fu (J. Sci. Comput., 2016)

A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. - Guosheng Fu; Chi-Wang Shu (J. Comput. Phys., 2017)

Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. - Bernardo Cockburn; Guosheng Fu; Francisco-Javier Sayas (Math. Comput., 2017)

A Systematic Construction of Finite Element Commuting Exact Sequences. - Bernardo Cockburn; Guosheng Fu (SIAM J. Numer. Anal., 2017)

Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations. - Mark Ainsworth; Guosheng Fu (J. Sci. Comput., 2018)

A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow. - Guosheng Fu; Christoph Lehrenfeld (J. Sci. Comput., 2018)

Discrete H1-Inequalities for Spaces Admitting M-Decompositions. - Bernardo Cockburn; Guosheng Fu; Weifeng Qiu (SIAM J. Numer. Anal., 2018)

A high-order HDG method for the Biot's consolidation model. - Guosheng Fu (Comput. Math. Appl., 2019)

Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces. - Guosheng Fu (CoRR, 2019)

An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation. - Guosheng Fu; Chi-Wang Shu (J. Comput. Appl. Math., 2019)

Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. - Guosheng Fu; Chi-Wang Shu (J. Comput. Phys., 2019)

Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation. - Mark Ainsworth; Guosheng Fu (J. Sci. Comput., 2019)

A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs. - Gang Chen 025; Guosheng Fu; John R. Singler; Yangwen Zhang (J. Sci. Comput., 2019)

An Explicit Divergence-Free DG Method for Incompressible Magnetohydrodynamics. - Guosheng Fu (J. Sci. Comput., 2019)

Detection of peripherally inserted central catheter (PICC) in chest X-ray images: A multi-task deep learning model. - Dingding Yu; Kaijie Zhang; Lingyan Huang; Bonan Zhao 002; Xiaoshan Zhang; Xin Guo; Miaomiao Li; Zheng Gu; Guosheng Fu; Minchun Hu; Yan Ping; Ye Sheng; et al. (Comput. Methods Programs Biomed., 2020)

Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity. - Guosheng Fu; Christoph Lehrenfeld; Alexander Linke; Timo Streckenbach (CoRR, 2020)

A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow. - Guosheng Fu (J. Comput. Phys., 2020)

POD-(H)DG Method for Incompressible Flow Simulations. - Guosheng Fu; Zhu Wang 003 (J. Sci. Comput., 2020)

Exact smooth piecewise polynomial sequences on Alfeld splits. - Guosheng Fu; Johnny Guzmán; Michael Neilan (Math. Comput., 2020)

Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for fluid-structure interaction. - Guosheng Fu (CoRR, 2021)

Uniform block diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes problem and linear elasticity. - Guosheng Fu; Wenzheng Kuang (CoRR, 2021)

High-order space-time finite element methods for the Poisson-Nernst-Planck equations: Positivity and unconditional energy stability. - Guosheng Fu; Zhiliang Xu (CoRR, 2021)

A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media. - Guosheng Fu; Yang Yang (CoRR, 2021)

A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations. - Lihong Feng; Guosheng Fu; Zhu Wang 003 (J. Sci. Comput., 2021)

Locking-Free and Gradient-Robust ${ varvec{H}}({{ , mathrm{{ text {div}}} , }})$-Conforming HDG Methods for Linear Elasticity. - Guosheng Fu; Christoph Lehrenfeld; Alexander Linke; Timo Streckenbach (J. Sci. Comput., 2021)

Uniform Auxiliary Space Preconditioning for HDG Methods for Elliptic Operators with a Parameter Dependent Low Order Term. - Guosheng Fu (SIAM J. Sci. Comput., 2021)

Optimal geometric multigrid preconditioners for HDG-P0 schemes for the reaction-diffusion equation and the generalized Stokes equations. - Guosheng Fu; Wenzheng Kuang (CoRR, 2022)

A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media. - Guosheng Fu; Yang Yang (CoRR, 2022)

A High-Order Velocity-Based Discontinuous Galerkin Scheme for the Shallow Water Equations: Local Conservation, Entropy Stability, Well-Balanced Property, and Positivity Preservation. - Guosheng Fu (J. Sci. Comput., 2022)

A Monolithic Divergence-Conforming HDG Scheme for a Linear Fluid-Structure Interaction Model. - Guosheng Fu; Wenzheng Kuang (SIAM J. Numer. Anal., 2022)

High order computation of optimal transport, mean field planning, and mean field games. - Guosheng Fu; Siting Liu 003; Stanley J. Osher; Wuchen Li (CoRR, 2023)

High-order variational Lagrangian schemes for compressible fluids. - Guosheng Fu; Chun Liu (CoRR, 2023)

Time-adaptive partitioned method for fluid-structure interaction problems with thick structures. - Martina Bukac; Guosheng Fu; Anyastassia Seboldt; Catalin Trenchea (J. Comput. Phys., 2023)

High-order variational Lagrangian schemes for compressible fluids. - Guosheng Fu; Chun Liu 009 (J. Comput. Phys., 2023)

High order computation of optimal transport, mean field planning, and potential mean field games. - Guosheng Fu; Siting Liu 003; Stanley J. Osher; Wuchen Li (J. Comput. Phys., 2023)

High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems. - Guosheng Fu; Stanley J. Osher; Wuchen Li (J. Comput. Phys., 2023)

Mean field control of droplet dynamics with high order finite element computations. - Guosheng Fu; Hangjie Ji; Will Pazner; Wuchen Li (CoRR, 2024)

A locally-conservative proximal Galerkin method for pointwise bound constraints. - Guosheng Fu; Brendan Keith; Rami Masri (CoRR, 2024)

Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. - Guosheng Fu; Stanley J. Osher; Will Pazner; Wuchen Li (J. Comput. Phys., 2024)

hp-Multigrid Preconditioner for a Divergence-Conforming HDG Scheme for the Incompressible Flow Problems. - Guosheng Fu; Wenzheng Kuang (J. Sci. Comput., 2024)

Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable. - Arjun Vijaywargiya; Guosheng Fu (J. Sci. Comput., 2024)

Efficient computation of mean field control based barycenters from reaction-diffusion systems. - Arjun Vijaywargiya; Guosheng Fu; Stanley J. Osher; Wuchen Li (J. Comput. Phys., 2025)

A four-field mixed formulation for incompressible finite elasticity. - Guosheng Fu; Michael Neunteufel; Joachim Schöberl; Adam Zdunek (CoRR, 2025)