Finite element methods for a singularly perturbed transmission problem

Finite element methods for a singularly perturbed transmission problem

We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high. We derive and analyze various finite element approaches for the approxi...

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Veröffentlicht in:Journal of numerical mathematics 2009-12, Vol.17 (4), p.245-275
Hauptverfasser: Nicaise, S., Xenophontos, C.
Format: Artikel
Sprache:eng
Schlagworte:
boundary layers
finite element method
transmission problems
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Beschreibung
Zusammenfassung:We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high. We derive and analyze various finite element approaches for the approximation of the solution and conduct numerical computations that show the robustness (or lack thereof) of each approach.
ISSN:1570-2820
1569-3953
DOI:10.1515/JNUM.2009.013