The Capriciousness of Numerical Methods for Singular Perturbations

The Capriciousness of Numerical Methods for Singular Perturbations

A collection of typical examples shows the exotic behavior of numerical methods when applied to singular perturbation problems. While standard meshes are used in the first six examples, even on layer-adapted meshes several surprising phenomena are shown to occur.

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Bibliographische Detailangaben
Veröffentlicht in:SIAM review 2011-01, Vol.53 (1), p.157-173
Hauptverfasser: Franz, Sebastian, Roos, Hans-Görg
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Boundary conditions
Boundary layers
Boundary value problems
Discrete problems
EDUCATION
Error rates
Exact sciences and technology
Finite element analysis
Galerkin methods
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods
Numerical methods in probability and statistics
Sciences and techniques of general use
Studies
Upwind schemes
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Beschreibung
Zusammenfassung:A collection of typical examples shows the exotic behavior of numerical methods when applied to singular perturbation problems. While standard meshes are used in the first six examples, even on layer-adapted meshes several surprising phenomena are shown to occur.
ISSN:0036-1445
1095-7200
DOI:10.1137/090757344