11 papers
A fifth-order absolutely convergent fixed-point fast sweeping hybrid alternative WENO scheme for steady state of hyperbolic conservation laws
Liang Li, Jun Zhu, Shanqin Chen +1
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-orde…
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…
An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws
Liang Li, Jun Zhu, Yong-Tao Zhang
High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high orde…