A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter ε{sup}2 is arbitrarily small, which induces boundary layers. We extend the numerical, method and its maximum norm error analysis of the paper [N. Kopteva: Math. Comp. 76 (2007) 631-646], in which a parametrization of the boundary {partial deriv}Ω is assumed to be known, to a more practical case when the domain is defined by an ordered set of boundary points. It is shown that, using layer-adapted meshes, one gets second-order convergence in the discrete maximum norm, uniformly in ε for ε≤Ch. Here h>0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch{sup}(-2). Numerical results are presented that support our theoretical error estimates.
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