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A weighted least squares method is given for the numerical solution of elliptic partial differential equations of Agmon-Douglis-Nirenberg type and an error analysis is provided. Some examples are given.

Summary.We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one-and two-dimensional problems are reported.

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