24 citations · 219 across the 39 of their papers we have counts for
37 papers · 1 filter
Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes
Guosheng Fu, Jian-Guo Liu
We develop an entropy-stable and physical-constraint-preserving discontinuous Galerkin spectral element method for symmetry-reduced general-relativistic hydrodynamics on prescribed…
Positivity-Preserving and Entropy-Stable Oscillation-Eliminating DGSEM for the Compressible Euler Equations on Curvilinear Meshes with Adaptive Mesh Refinement
Jielin Yang, Jieling Yang, Guosheng Fu
We extend the entropy-stable oscillation-eliminating discontinuous Galerkin spectral element method (ES-OEDG) on curvilinear meshes \cite{YangFu26} to adaptive mesh refinement (AMR…
Two Finite Element Approaches For The Porous Medium Equation That Are Positivity Preserving And Energy Stable
Arjun Vijaywargiya, Guosheng Fu
In this work, we present the construction of two distinct finite element approaches to solve the Porous Medium Equation (PME). In the first approach, we transform the PME to a log-…
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems
Guosheng Fu, Stanley Osher, Wuchen Li
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metr…
-Multigrid preconditioner for a divergence-conforming HDG scheme for the incompressible flow problems
Guosheng Fu, Wenzheng Kuang
In this study, we present an -multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagr…
High-order variational Lagrangian schemes for compressible fluids
Guosheng Fu, Chun Liu
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/mome…
High order computation of optimal transport, mean field planning, and mean field games
Guosheng Fu, Siting Liu, Stanley Osher +1
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However,…
A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
Guosheng Fu, Yang Yang
We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous media. In particular we apply the HDG metho…
Optimal geometric multigrid preconditioners for HDG-P0 schemes for the reaction-diffusion equation and the generalized Stokes equations
Guosheng Fu, Wenzheng Kuang
We present the lowest-order hybridizable discontinuous Galerkin schemes with numerical integration (quadrature), denoted as HDG-P0, for the reaction-diffusion equation and the gene…
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
We present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bott…
A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
Guosheng Fu, Yang Yang
We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated…
High-order space-time finite element methods for the Poisson-Nernst-Planck equations: Positivity and unconditional energy stability
Guosheng Fu, Zhiliang Xu
We present a novel class of high-order space-time finite element schemes for the Poisson-Nernst-Planck (PNP) equations. We prove that our schemes are mass conservative, positivity…
Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations
Guosheng Fu, Wenzheng Kuang
We propose a uniform block-diagonal preconditioner for condensed (div)-conforming HDG schemes for parameter-dependent saddle point problems, including the generalized Stokes equ…
Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for fluid-structure interaction
Guosheng Fu
We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes…
A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations
Lihong Feng, Guosheng Fu, Zhu Wang
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate the…
A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model
Guosheng Fu, Wenzheng Kuang
We present a novel monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction (FSI) problem with a thick structure. A pressure-robust optimal energy-norm…
Uniform auxiliary space preconditioning for HDG methods for elliptic operators with a parameter dependent low order term
Guosheng Fu
The auxiliary space preconditioning (ASP) technique is applied to the HDG schemes for three different elliptic problems with a parameter dependent low order term, namely, a symmetr…
POD-(H)DG Method for Incompressible Flow Simulations
Guosheng Fu, Zhu Wang
We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized…
A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow
Guosheng Fu
We construct a divergence-free HDG scheme for the Cahn-Hilliard-Navier-Stokes phase field model. The scheme is robust in the convection-dominated regime, produce a globally diverge…
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
Guosheng Fu, Christoph Lehrenfeld, Alexander Linke +1
Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be…
Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces
Guosheng Fu
We present a class of Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for the incompressible flow with moving boundaries and interfaces including two-phas…
A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs
Gang Chen, Guosheng Fu, John Richard Singler +1
We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018…
An explicit divergence-free DG method for incompressible magnetohydrodynamics
Guosheng Fu
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A global…
An explicit divergence-free DG method for incompressible flow
Guosheng Fu
We present an explicit divergence-free DG method for incompressible flow based on velocity formulation only. A globally divergence-free finite element space is used for the velocit…