Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a
strict maximum principle for general nonlinear convection–diffusion equations on …

In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods
[8],[9],[19],[21] for convection diffusion equations on unstructured triangular mesh. We …

We consider solving a generalized Allen-Cahn equation coupled with a passive convection
for a given incompressible velocity field. The numerical scheme consists of the first order …

In this paper, we construct a high order weighted essentially non-oscillatory (WENO) finite
difference discretization for compressible Navier-Stokes (NS) equations, which is rendered …

In this paper, we construct a positivity-preserving high order accurate finite volume hybrid
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …

Since proposed in Zhang and Shu (2010)[1], the Zhang–Shu framework has attracted
extensive attention and motivated many bound-preserving (BP) high-order discontinuous …

In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP)
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …

We design and analyze up to third order accurate discontinuous Galerkin (DG) methods
satisfying a strict maximum principle for Fokker--Planck equations. A procedure is …