2 citations · 4 across the 11 of their papers we have counts for
12 papers
A Local Discontinuous Galerkin method for the modified Camassa--Holm equation
Xiang-Ke Chang, Yong Liu, Qi Tao
In this paper, we propose a local discontinuous Galerkin (LDG) method for the modified Camassa-Holm (mCH) equation that contains cubic nonlinearity and high-order derivative terms.…
The error estimate of entropy-stable discontinuous Galerkin methods for hyperbolic conservation laws
Xu-Kun Chen, Yong Liu, Chi-Wang Shu
Entropy inequalities are fundamental to the well-posedness of hyperbolic conservation laws, providing the essential criterion for selecting the physically admissible solution among…
Weighted Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Methods for Conservation Laws
Yongjie Bi, Yan Jiang, Yong Liu
In this paper, we propose a weighted inverse Lax-Wendroff (WILW) boundary treatment for the discontinuous Galerkin (DG) method on unfitted meshes to efficiently solve hyperbolic co…
An Interior Penalty Discontinuous Galerkin Method for an Interface Model of Flow in Fractured Porous Media
Yong Liu, Ziyao Xu
Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, nume…
An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces
Zhiming Chen, Yong Liu
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curv…
Efficient and Parallel Solution of High-order Continuous Time Galerkin for Dissipative and Wave Propagation Problems
Zhiming Chen, Yong Liu
We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legend…
A high order explicit time finite element method for the acoustic wave equation with discontinuous coefficients
Zhiming Chen, Yong Liu, Xueshuang Xiang
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having comple…
An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations
Qi Tao, Yong Liu, Yan Jiang +1
In this paper, we develop an oscillation free local discontinuous Galerkin (OFLDG) method for solving nonlinear degenerate parabolic equations. Following the idea of our recent wor…
A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations
Yong Liu, Jianfang Lu, Qi Tao +1
In this paper, we develop a well-balanced oscillation-free discontinuous Galerkin (OFDG) method for solving the shallow water equations with a non-flat bottom topography. One notab…
A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations
Juntao Huang, Yong Liu, Yuan Liu +2
In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear dispers…
Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations
Yong Liu, Chi-Wang Shu, Mengping Zhang
In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes have s…
Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension
Anqi Chen, Yingda Cheng, Yong Liu +1
We analyze the superconvergence properties of ultra-weak discontinuous Galerkin (UWDG) methods with various choices of flux parameters for one-dimensional linear Schrödinger equati…