{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:08Z","timestamp":1787329268440,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/060677616","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T18:09:04Z","timestamp":1207937344000},"page":"1602-1618","source":"Crossref","is-referenced-by-count":28,"title":["Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem"],"prefix":"10.1137","volume":"46","author":[{"given":"Natalia","family":"Kopteva","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,11]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"M. Abramowitz and I. A. 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