An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn–Hilliard–Brinkman system

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

“…We list below only a few examples over the past year (since 2015). Recent applications of DG methods can be found in the simulations of the Cahn-Hilliard-Brinkman system [85], compressible flow in the transonic axial compressor [190], computational astrophysics [197], computational geosciences [221], elastodynamics [53], flow instabilities [51], Fokker-Planck equations [152], fractional PDEs [111,243], front propagation with obstacles [17], functionalized Cahn-Hilliard equation [87], interfaces [278], magnetohy-drodynamics [265], moment closures for kinetic equations [2], multi-phase flow and phase transition [52,169], Navier-Stokes and Boussinesq equations [64,224], nonlinear Schrodinger equation [86,149,158], ocean waves [192], population models [112], porous media [84], rarefied gas [212], semiconductor device simulation [155], shallow water equations [73], thin film epitaxy problem [247], traffic flow and networks [21], three-dimensional flows [175], turbulent flows [246], underwater explosion [235], viscous surface wave [245], and wavefield modeling [95]. This very incomplete list over just one year period clearly demonstrates the wide-spread application of the DG method in computational science and engineering.…”