35 citations · 127 across the 19 of their papers we have counts for
19 papers
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…
High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity
Guanlan Huang, Yulong Xing, Tao Xiong
In this paper, we propose a high order semi-implicit well-balanced finite difference scheme for all Mach Euler equations with a gravitational source term. To obtain the asymptotic…
Energy conserving and well-balanced discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry
Weijie Zhang, Yulong Xing, Eirik Endeve
This paper presents high-order Runge-Kutta (RK) discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry. The scheme can preserve a general polytropic e…
Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise
Jiawei Sun, Chi-Wang Shu, Yulong Xing
In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The disc…
Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise
Jiawei Sun, Chi-Wang Shu, Yulong Xing
One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic struct…
Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system
Jiawei Sun, Shusen Xie, Yulong Xing
Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equat…
High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
Guanlan Huang, Yulong Xing, Tao Xiong
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom t…
Finite Element Approximations of a Class of Nonlinear Stochastic Wave Equation with Multiplicative Noise
Yukun Li, Shuonan Wu, Yulong Xing
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the medi…
High order finite difference Hermite WENO fixed-point fast sweeping method for static Hamilton-Jacobi equations
Yupeng Ren, Yulong Xing, Jianxian Qiu
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilt…
High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state transport equation
Yupeng Ren, Yulong Xing, Dean Wang +1
In this paper, we propose to combine the fifth order Hermite weighted essentially non-oscillatory (HWENO) scheme and fast sweeping method (FSM) for the solution of the steady-state…
High order finite difference Hermite WENO fast sweeping methods for static Hamilton-Jacobi equations
Yupeng Ren, Yulong Xing, Jianxian Qiu
In this paper, we propose a novel Hermite weighted essentially non-oscillatory (HWENO) fast sweeping method to solve the static Hamilton-Jacobi equations efficiently. During the HW…
Recovery of a Time-Dependent Bottom Topography Function from the Shallow Water Equations via an Adjoint Approach
Jolene Britton, Yat Tin Chow, Weitao Chen +1
We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, name…
Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness
Kailiang Wu, Yulong Xing
This paper presents a class of novel high-order accurate discontinuous Galerkin (DG) schemes for the compressible Euler equations under gravitational fields. A notable feature of t…
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…
Analysis of mixed interior penalty discontinuous Galerkin methods for the Cahn-Hilliard equation and the Hele-Shaw flow
Xiaobing Feng, Yukun Li, Yulong Xing
This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods u…
On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations
Yulong Xing, Chi-Wang Shu, Sebastian Noelle
This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numeri…
Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates
Eirik Endeve, Cory D. Hauck, Yulong Xing +1
We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. T…
Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number
Xiaobing Feng, Yulong Xing
Two local discontinuous Galerkin (LDG) methods using some non-standard numerical fluxes are developed for the Helmholtz equation with the first order absorbing boundary condition i…