5 papers
TVD and TVB preservation without TVD time discretization for discontinuous Galerkin methods
Ziyao Xu, Zheng Sun
Total variation diminishing (TVD) and total variation bounded (TVB) properties are crucial for controlling spurious oscillations in numerical solutions of conservation laws. In the…
A Conservative and Positivity-Preserving Discontinuous Galerkin Method for the Population Balance Equation
Ziyao Xu, Guanyang Liu, Yong-Tao Zhang
We develop a conservative, positivity-preserving discontinuous Galerkin (DG) method for the population balance equation (PBE), which models the distribution of particle numbers acr…
Exponential Time Differencing Runge-Kutta Discontinuous Galerkin (ETD-RKDG) Methods for Nonlinear Degenerate Parabolic Equations
Ziyao Xu, Yong-Tao Zhang
In this paper, we study high-order exponential time differencing Runge-Kutta (ETD-RK) discontinuous Galerkin (DG) methods for nonlinear degenerate parabolic equations. This class o…
Stability and Time-Step Constraints of Exponential Time Differencing Runge--Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations
Ziyao Xu, Zheng Sun, Yong-Tao Zhang
In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge-Kutta (RK) methods i…
High-order exponential time differencing multi-resolution alternative finite difference WENO methods for nonlinear degenerate parabolic equations
Ziyao Xu, Yong-Tao Zhang
In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes i…