80 citations · 108 across the 12 of their papers we have counts for
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Fully discrete multi-entropy-stable compact Runge--Kutta discontinuous Galerkin methods for hyperbolic conservation laws
Zheng Sun
We develop fully discrete multi-entropy-stable high-order compact Runge--Kutta discontinuous Galerkin (cRKDG) methods for hyperbolic conservation laws. Our main result is a weak ce…
On Energy Laws and Stability of First-Subdiagonal Pade Approximants for Linear Seminegative Problems
Miaosen Jiao, Zheng Sun, Kailiang Wu
We derive an explicit discrete energy identity for rational time discretizations generated by the first-subdiagonal Padé approximants of the exponential for solving linear seminega…
The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws
Qifan Chen, Zheng Sun, Yulong Xing
In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the trad…
On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix
Zheng Sun, Yulong Xing
In this paper, we study a numerical artifact of solving the nonlinear shallow water equations with a discontinuous bottom topography. For various first-order schemes, the numerical…
The Runge--Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws
Qifan Chen, Zheng Sun, Yulong Xing
In this paper, we develop a new type of Runge--Kutta (RK) discontinuous Galerkin (DG) method for solving hyperbolic conservation laws. Compared with the original RKDG method, the n…
Stability of structure-aware Taylor methods for tents
Jay Gopalakrishnan, Zheng Sun
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are usefu…
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
Zheng Sun, Yuanzhe Wei, Kailiang Wu
This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge--Kutta (RK) methods for linear seminegative systems. I…
Error analysis of Runge--Kutta discontinuous Galerkin methods for linear time-dependent partial differential equations
Zheng Sun, Chi-Wang Shu
In this paper, we present error estimates of fully discrete Runge--Kutta discontinuous Galerkin (DG) schemes for linear time-dependent partial differential equations. The analysis…
On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: Energy conservation and multi-symplecticity
Zheng Sun, Yulong Xing
In this paper, we present and study discontinuous Galerkin (DG) methods for one-dimensional multi-symplectic Hamiltonian partial differential equations. We particularly focus on se…
Enforcing strong stability of explicit Runge--Kutta methods with superviscosity
Zheng Sun, Chi-Wang Shu
A time discretization method is called strongly stable, if the norm of its numerical solution is nonincreasing. It is known that, even for linear semi-negative problems, many expli…
Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport
Zheng Sun, Cory D. Hauck
The discrete ordinates discontinuous Galerkin (-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a…
Strong stability of explicit Runge-Kutta time discretizations
Zheng Sun, Chi-Wang Shu
Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge-Kutta (…
An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems
Zheng Sun, José Antonio Carrillo, Chi-Wang Shu
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure.…
A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
Zheng Sun, José A. Carrillo, Chi-Wang Shu
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence…