Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments

Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

(2010) Yulong Xing et al.   ADVANCES IN WATER RESOURCES

A New Class of Nonlinear Finite-Volume Methods for Vlasov Simulation

(2010) Jeffrey William Banks et al.   IEEE TRANSACTIONS ON PLASMA SCIENCE

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On maximum-principle-satisfying high order schemes for scalar conservation laws

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws

(2010) Xiangxiong Zhang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

(2009) Chi-Wang Shu   SIAM REVIEW