Diffusive BGK approximations for nonlinear multidimensional parabolic equations

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Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations (2012, background): “1) and its variants, see [1,4,6,9,10,12,21] and the references cited therein.”
Upwind difference approximations for degenerate parabolic convection–diffusion equations with a discontinuous coefficient (2002, methodology): “Let us mention the operator splitting methods in [16, 24], the finite difference schemes in [18, 15, 17], the finite volume schemes in [1, 40, 20], and the kinetic BGK schemes in [3].”
QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS (2005, background): “The question of convergence of numerical schemes in the isotropic diffusion case has also been addressed in a series of papers by different authors; see [1, 5, 19, 20, 23, 25, 31, 32] and the references cited therein.”
Operator splitting methods for degenerate convection–diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation (2000, methodology): “For related work on numerical methods for strongly degenerate parabolic equations, see Evje and Karlsen [22‐25] for upwind difference schemes; Kurganov and Tadmor [37] for central difference schemes; and Bouchut et al. [ 5 ] for kinetic BGK schemes.”