Discrete maximum principles for nonlinear parabolic PDE systems

Discrete Maximum Principles for Nonlinear Parabolic PDE Systems

Discrete maximum principles for nonlinear parabolic

Discrete maximum principles are established for finite element approximations 10 of nonlinear parabolic PDE systems with mixed boundary and interface conditions. The 11 results are based on an algebraic discrete maximum principle for suitable ODE systems. 12

A discrete model for an ill-posed nonlinear parabolic PDE

We study a finite-difference discretization of an ill-posed nonlinear parabolic partial differential equation. The PDE is the one-dimensional version of a simplified two-dimensional model for the formation of shear bands via anti-plane shear of a granular medium. For the discretized initial value problem, we derive analytically, and observed numerically, a two-stage evolution leading to a stead...

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

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.

On discrete maximum principles for nonlinear elliptic problems