Reaction-Diffusion-Advection Systems with Discontinuous Diffusion and Mass Control

Discontinuous Galerkin Methods for Advection-diffusion-reaction Problems

We apply the weighted-residual approach recently introduced in [7] to derive dis-continuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods. 1. Introduction. In recent years Discontinuous Galerkin methods have become increasingly popular, and they have ...

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

Optimal Stretching in Advection-Reaction-Diffusion Systems.

We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted...

Stable advection-reaction-diffusion with arbitrary anisotropy

Turing first theorized that many biological patterns arise through the processes of reaction and diffusion [1]. Subsequently, reaction-diffusion systems have been studied in many fields, including computer graphics. We first show that for visual simulation purposes, reaction-diffusion equations can be made unconditionally stable using a variety of straightforward methods. Second, we propose an ...

Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection

We construct and analyze a discontinuous Galerkin method to solve advectiondiffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consiste...