Record link: 
http://hdl.handle.net/20.500.12708/147528
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Title: 
Robust exponential convergence of 𝒉𝒑-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains
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Citation: 
Faustmann, M., & Melenk, J. M. (2017). Robust exponential convergence of 𝒉𝒑-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains. Computers and Mathematics with Applications, 74(7), 1576–1589. https://doi.org/10.1016/j.camwa.2017.03.015
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Publisher DOI: 
10.1016/j.camwa.2017.03.015
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Faustmann, Markus 
Melenk, Jens Markus 
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Organisational Unit: 
E101-02 - Forschungsbereich Numerik 
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Journal: 
Computers and Mathematics with Applications 
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ISSN: 
0898-1221
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Date (published): 
1-Oct-2017
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Number of Pages: 
14
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Publisher: 
PERGAMON-ELSEVIER SCIENCE LTD
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Peer reviewed: 
Yes
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Keywords: 
Modeling and Simulation; Computational Mathematics; Computational Theory and Mathematics; Singular perturbation; High order FEM; Balanced norm; Uniform estimates
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Abstract: 
The hp-version of the finite element method is applied to singularly perturbed reaction-diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitably refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.
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Research Areas: 
Mathematical and Algorithmic Foundations: 70%
Modelling and Simulation: 30%
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Science Branch: 
Mathematik
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