A multiscale a posteriori error estimate |
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Affiliation: | 2. LNCC, Laboratório Nacional de Computação, Cientı́fica, Av. Getúlio Vargas, 333, 25651-070 Petrópolis, RJ, Brazil;1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trabalhador São-carlense, 400, 13566-590, São Carlos, SP, Brazil;2. Department of Mathematical Sciences, The University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080-3021, USA |
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Abstract: | We introduce a hierarchic a posteriori error estimate for singularly perturbed reaction–diffusion problems. The estimator is based on a Petrov–Galerkin method in which the trial space is enriched with nonpolynomial functions or multiscale functions. We study the equivalence between the a posteriori estimate and the exact error in the energy norm. Moreover, we prove a relationship between the hierarchic estimator and an explicit residual estimator. The approach provides accurate estimates for the boundary layer regions which is confirmed by numerical experiments. |
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