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Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem. (English) Zbl 1149.65066
A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. This paper presents second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support the theoretical estimates.

MSC:
65L70 Error bounds for numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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