Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling

Abstract

Discrete nonnegativity principles are established for finite element approximations of nonlinear parabolic PDE systems with mixed boundary conditions. Previous results of the authors are extended such that diagonal dominance (or essentially monotonicity) of the nonlinear coupling can be relaxed, allowing to include much more general situations in suitable models. © 2016 International Association for Mathematics and Computers in Simulation (IMACS).