8 papers
Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements
Siyuan Fan, Guosheng Fu
We develop a high-order, fully explicit operator-splitting method for 2.5D ideal magnetohydrodynamics on Cartesian meshes. The hydrodynamic subflow is advanced by an entropy-stable…
An entropy-stable oscillation-eliminating dgsem for the euler equations on curvilinear meshes
Jielin Yang, Guosheng Fu
We develop an entropy-stable high-order numerical method for the two-dimensional compressible Euler equations on general curvilinear meshes. The proposed approach is based on a nod…
The proximal Galerkin method for non-symmetric variational inequalities
Guosheng Fu, Brendan Keith, Dohyun Kim +2
We introduce the proximal Galerkin (PG) method for non-symmetric variational inequalities. The proposed approach is asymptotically mesh-independent and yields constraint-preserving…
A Schrödinger-Based Dispersive Regularization Approach for Numerical Simulation of One-Dimensional Shallow Water Equations
Guosheng Fu, Chun Liu
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regular…
Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis
Zecheng Zhang, Hao Liu, Guosheng Fu +2
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from inp…
A four-field mixed formulation for incompressible finite elasticity
Guosheng Fu, Michael Neunteufel, Joachim Schöberl +1
In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [Gopalakrishnan J., Lederer P., and Schöberl J., A mass conserving mix…
A locally-conservative proximal Galerkin method for pointwise bound constraints
Guosheng Fu, Brendan Keith, Rami Masri
We introduce the first-order system proximal Galerkin (FOSPG) method, a locally mass-conserving, hybridizable finite element method for solving heterogeneous anisotropic diffusion…
Discrete -inequalities for spaces admitting M-decompositions
Bernardo Cockburn, Guosheng Fu, Weifeng Qiu
We find new discrete - and Poincaré-Friedrichs inequalities by studying the invertibility of the DG approximation of the flux for local spaces admitting M-decompositions. We t…