9 problems

The compressible Navier--Stokes--Allen--Cahn system admits an equivalent reformulation in which the nonlinear variational derivatives of the free energy belong to the discontinuous…

The CSLDG method is a semi-Lagrangian discontinuous Galerkin scheme for transport equations; its numerical experiments exhibit both superconvergence and fluctuations in convergence…

Consider the discontinuous Galerkin methods for the vector-invariant spherical shallow water equations described in the paper, and compare their convergence with the optimal fourth…

Let $H(u(\cdot,t_0),\tau)$ denote an exact solution operator mapping an initial condition $u(\cdot,t_0)$ to the solution at time $t_0+\tau$. Let $V$ be the finite-dimensional appro…

Taylor time-stepping methods have local stability radii that do not yield an order-independent CFL number. Stability-enhanced Taylor-scheme conjecture. Stability-enhanced schemes c…

The full-order model (FOM) uses global proper orthogonal decomposition (POD) bases, and the conservative POD-DG model is observed to have better stability properties than the conse…

Normal-continuity conjecture. The improved accuracy for $m=k$ is due to a better enforcement of continuity of the normal component of the velocity.

The semi-Lagrangian method advances a solution through repeated time steps, using either a discontinuous Galerkin scheme or interpolation methods such as Lagrange and spline interp…

Geometric-assumption conjecture. The results of the paper could be proved without using the geometric assumption on the mixed boundary.