24 citations · 219 across the 39 of their papers we have counts for
9 papers · 1 filter
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…
Exact smooth piecewise polynomial sequences on Alfeld splits
Guosheng Fu, Johnny Guzman, Michael Neilan
We develop exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vert…
Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation
Mark Ainsworth, Guosheng Fu
The dispersive behavior of the recently proposed energy-conserving discontinuous Galerkin (DG) method by Fu and Shu [10] is analyzed and compared with the classical centered and up…
An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation
Guosheng Fu, Chi-Wang Shu
We propose an energy-conserving ultra-weak discontinuous Galerkin (DG) method for the generalized Korteweg-De Vries(KdV) equation in one dimension. Optimal a priori error estimate…
Bernstein-Bezier Bases for Tetrahedral Finite Elements
Mark Ainsworth, Guosheng Fu
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are e…
A high-order HDG method for the Biot's consolidation model
Guosheng Fu
We propose a novel high-order HDG method for the Biot's consolidation model in poroelasticity. We present optimal error analysis for both the semi-discrete and full-discrete (combi…
Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems
Guosheng Fu, Chi-Wang Shu
We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order $…