Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle

We present a method to approximate (in any space dimension) diffusion equations with schemes having a specific structure; this structure ensures that the discrete local maximum and minimum principles are respected, and that no spurious oscillations appear in the solutions. When applied in a transient setting on models of concentration equations, it guaranties in particular that the approximate solutions stay between the physical bounds. We make a theoretical study of the constructed schemes, proving under a coercivity assumption that their solutions converge to the solution of the PDE. Several numerical results are also provided; they help us understand how the parameters of the method should be chosen. These results also show the practical efficiency of the method, even when applied to complex models. Key words. finite volumes, anisotropic heterogeneous diffusion, maximum principle, convergence study, numerical tests AMS subject classifications. 65N08, 65N12 DOI. 10.1137/09077084...

• Type: Journal
• Year: 2011
• Where: SIAMNUM
• Authors: Jérôme Droniou, Christophe Le Potier
• Keywords: Discrete Local Maximum, Numerical Tests Ams, SIAMNUM 2011, Software Engineering, Solution