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

Natalia Kopteva

doi:10.1007/978-3-319-67202-1_11

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

Natalia Kopteva

Department of Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016
Editors	Martin Stynes, Zhimin Zhang, Zhongyi Huang
Publisher	Springer Verlag
Pages	141-154
Number of pages	14
ISBN (Print)	9783319672014
DOIs	https://doi.org/10.1007/978-3-319-67202-1_11
Publication status	Published - 2017
Event	International Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2016 - Beijing, China Duration: 15 Aug 2016 → 19 Aug 2016

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	120
ISSN (Print)	1439-7358

Conference

Conference	International Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2016
Country/Territory	China
City	Beijing
Period	15/08/16 → 19/08/16

Access to Document

10.1007/978-3-319-67202-1_11

Cite this

Kopteva, N. (2017). Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions. In M. Stynes, Z. Zhang, & Z. Huang (Eds.), Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016 (pp. 141-154). (Lecture Notes in Computational Science and Engineering; Vol. 120). Springer Verlag. https://doi.org/10.1007/978-3-319-67202-1_11

Kopteva, Natalia. / Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes : Neumann Boundary Conditions. Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. editor / Martin Stynes ; Zhimin Zhang ; Zhongyi Huang. Springer Verlag, 2017. pp. 141-154 (Lecture Notes in Computational Science and Engineering).

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

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.",

author = "Natalia Kopteva",

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year = "2017",

doi = "10.1007/978-3-319-67202-1_11",

language = "English",

isbn = "9783319672014",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "141--154",

editor = "Martin Stynes and Zhimin Zhang and Zhongyi Huang",

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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 M Stynes, Z Zhang & Z Huang (eds), Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. Lecture Notes in Computational Science and Engineering, vol. 120, Springer Verlag, pp. 141-154, International Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2016, Beijing, China, 15/08/16. https://doi.org/10.1007/978-3-319-67202-1_11

Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions. / Kopteva, Natalia.
Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. ed. / Martin Stynes; Zhimin Zhang; Zhongyi Huang. Springer Verlag, 2017. p. 141-154 (Lecture Notes in Computational Science and Engineering; Vol. 120).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

AB - 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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Kopteva N. Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions. In Stynes M, Zhang Z, Huang Z, editors, Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. Springer Verlag. 2017. p. 141-154. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-67202-1_11

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

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