DDFV scheme for nonlinear parabolic reaction-diffusion problems on general meshes
This paper focuses on the nonlinear anisotropic parabolic model of the form $\partial_{t}C(u)-\operatorname{div}(\Lambda \nabla u)+ R(u)=f$, where $C$, $R$, $f$, and $\Lambda$ are respectively: two nonlinear functions, a source term and an anisotropic tensor diffusion. For space discretization, various types of the Discrete Duality Finite Volume (DDFV) scheme are elaborated leading to positive definite stiffness matrices for the diffusion term. A general mesh is used and hard anisotropic tensor with discontinuous effects is considered. An implicit time scheme is deve