Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes

摘要: For the case of approximation convection---diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes scheme satisfy discrete maximum principle. The shown to be Lipschitz and linearity preserving. Using these properties we provide full stability error analysis, which, in dominated regime, shows existence, uniqueness optimal convergence. Then algebraic flux correction method recalled show present can interpreted as an for particular definition limiters. performance illustrated on some numerical test cases two space dimensions.