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

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 Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the no...

Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE

We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...

ar X iv : 0 90 6 . 14 58 v 1 [ m at h . A P ] 8 J un 2 00 9 DIFFERENCE - QUADRATURE SCHEMES FOR NONLINEAR DEGENERATE PARABOLIC INTEGRO - PDE

We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...

Discrete Maximum Principles for Nonlinear Parabolic PDE Systems