Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem

Kopteva, Natalia (2008) Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem. SIAM Journal on Numerical Analysis, 46 (3). pp. 1602-1618. ISSN 0036-1429

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    Abstract

    A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate