Relaxed Schemes Based on Diffusive Relaxation for Hyperbolic-Parabolic Problems: Some New Developments

In this work we briefly survey the numerical solution of non linear convection diffusion equations using relaxed methods. We consider several approaches to the construction of approximating relaxation systems, studying the numerical properties of the resulting relaxed schemes. The unified approach proposed here includes BGK-based diffusive relaxation methods, but also allows for the construction of new relaxed methods. A stability analysis for the new methods is sketched and high order extensions are provided. Finally several numerical tests in one and two dimensions are shown.