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Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions

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Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 120))

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Abstract

Residual-type a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. The case of the Dirichlet boundary conditions was considered in the recent article (Kopteva, Numer. Math., 2017, Published online 2 May 2017. doi:10.1007/s00211-017-0889-3). Now we extend this analysis to also allow boundary conditions of Neumann type.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

    Natalia Kopteva

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  1. Natalia Kopteva
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Correspondence to Natalia Kopteva .

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Editors and Affiliations

  1. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Zhongyi Huang

  2. Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing, China

    Martin Stynes

  3. Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing, China

    Zhimin Zhang

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Kopteva, N. (2017). Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions. In: Huang, Z., Stynes, M., Zhang, Z. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. Lecture Notes in Computational Science and Engineering, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-67202-1_11

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