Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations

Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations

(2021) Lili Ju et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models

(2020) Yuezheng Gong et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On the maximum principle preserving schemes for the generalized Allen–Cahn equation

(2016) Jie Shen et al.   Communications in Mathematical Sciences

Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle

(2016) Tao Tang et al.   JOURNAL OF COMPUTATIONAL MATHEMATICS

Maximum-Principle-Satisfying Third Order Discontinuous Galerkin Schemes for Fokker--Planck Equations

(2014) Hailiang Liu et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and Lubrication-type equations

(2013) Changna Lu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem

(2013) Zhengfu Xu   MATHEMATICS OF COMPUTATION

A note on why enforcing discrete maximum principles by a simple a posteriori cutoff is a good idea

(2013) Christian Kreuzer   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

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

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