Open access
Date
1997-02Type
- Report
ETH Bibliography
yes
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Abstract
A singularly perturbed reaction-diffusion equation in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve and the right hand side is analytic. We show that the hp version of the finite element method leads to robust exponential convergence provided that one layer of needle elements of width $O(p \varepsilon)$ is inserted near the domain boundary, that is, the rate of convergence is $O({ exp} (-b p))$ and independent of the perturbation parameter $\varepsilon$. We also show that the Spectral Element Method based on the use of a Gauss-Lobatto quadrature rule of order O(p) for the evaluation of the stiffness matrix and the load vector retains the exponential rate of convergence. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004317902Publication status
publishedJournal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Boundary layer; Singularly perturbed problem; Asymptotic expansions; Error boundsOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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Is continued by: https://doi.org/10.3929/ethz-b-000566850
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ETH Bibliography
yes
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