We show that the classical fourth order accurate compact finite difference scheme with high
order strong stability preserving time discretizations for convection diffusion problems …

For the initial value problem of scalar conservation laws, a bound-preserving property is
desired for numerical schemes in many applications. Traditional methods to enforce a …

We analyze the properties and compare the performance of several positivity limiters for
spectral approximations with respect to the angular variable of linear transport equations. It …

High-order accurate weighted essentially non-oscillatory (WENO) schemes are a class of
broadly applied numerical methods for solving hyperbolic partial differential equations …

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars
advected by them, on staggered grids. In contrast to existing WENO schemes on staggered …

On rectangular meshes, the simplest spectral element method for elliptic equations is the
classical Lagrangian Q k finite element method with only (k+ 1)-point Gauss-Lobatto quadra …