Research Reports

Research Reports

Numerical study on the convergence to steady state solutions of a new class of finite volume WENO schemes:  triangular meshes.  Jun Zhu and Chi-Wang Shu. 

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes.  Yong Liu, Chi-Wang Shu and Mengping Zhang.

Bound_preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar conservation laws with stiff source terms, Juntao Huang and Chi-Wang Shu.

Discontinuous-Galerkin Methods for a Kinetic Model of Self-Organized Dynamics, Francis Filbet and Chi-Wang Shu.

On the convergence to steady state solutions of a new class of high order WENO schemes, Jun Zhu and Chi-Wang Shu.

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, Zheng Sun, Jose A. Carillo and Chi-Wang Shu.

Implicit positivity preserving high order discontinuous Galerkin methods for conservation laws, Tong Qin and Chi-Wang Shu.

Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates, Dan Ling, Juan Cheng, and Chi-Wang Shu.

On local conservation of numerical methods for conservation laws, Cengke Hi and Chi-Wang Shu.

On the time growth of the error of the DG method for advective problems,  Václav Kučera and Chi-Wang Shu.

Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation, Huailing Song and Chi-Wang Shu.

A New Trouble-Cell Indicator for Discontinuous Galerkin Methods for Hyperbolic Conservation Laws, Guosheng Fu and Chi-Wang Shu.

Entropy stable high order discontinuous Galerkin methods with suitable
quadrature rules for hyperbolic conservation laws
, Tianheng Chen and Chi-Wang Shu