Nodal discrete duality numerical scheme for nonlinear diffusion problems on general meshes

Abstract Discrete duality finite volume (DDFV) schemes are known for their ability to approximate nonlinear and linear anisotropic diffusion operators on general meshes, but they possess several drawbacks. The most important drawback of DDFV is the simultaneous use cell node unknowns. We propose a discretization approach that incorporates ideas associated analysis techniques, allows rapid elimination Further, unlike scheme, new ‘Nodal Duality’ (NDD) scheme does not require specific adaptation in presence discontinuities tensor along boundaries. describe detail 2D NDD framework its two 3D variants, focusing consistency properties discrete gradient divergence key structural property duality. For convergence carried out series numerical tests provided large family elliptic problems with zero Dirichlet boundary condition.