Numerical Methods for Reaction-Diffusion Problems with Non-Differentiable Kinetics

摘要

This document considers a class of steady-state semi-linear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. The first step in analyzing their numerical approximation is taken. The authors present a finite element method and establish error bounds which are optimal for some of the problems. In addition, a finite difference approach is also discussed. Numerical experiments for one-and two-dimensional problems are reported. (Author)