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\r\nconvection diffusion equations using relaxed methods. We consider several\r\napproaches to the construction of approximating relaxation systems,\r\nstudying the numerical properties of the resulting relaxed schemes. The\r\nunified approach proposed here includes BGK-based diffusive relaxation\r\nmethods, but also allows for the construction of new relaxed methods.\r\nA stability analysis for the new methods is sketched and high order extensions\r\nare provided. Finally several numerical tests in one and two\r\ndimensions are shown.