In this paper, we apply discontinuous Galerkin (DG) methods to solve two model equations: Krause's consensus models and pressureless Euler equations. These two models are used to describe the collisions of particles, and the distributions can be identified as density functions. If the particles are placed at a single point, then the density function turns… (More)
In this paper, we develop discontinuous Galerkin (DG) methods to solve ideal special relativistic hydrodynamics (RHD). In RHD, the density and pressure are positive. Units are normalized so that the speed of light is c = 1. Therefore, the velocity of the fluid has magnitude less than 1. To construct physically relevant numerical approximations, we develop a… (More)
We derive the lower bound of the penalty parameter in the C 0 IPDG for the bi-harmonic equation. Based on the bound, we propose a pre-processing algorithm. Numerical example are shown to support the theory. In addition, we found that an optimal penalty does exist.