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Adaptive approximation. (English) Zbl 0652.65062
Der Autor definiert Adaptivität als eine Auswahlstrategie, die unter Verwendung eines monotonen lokalen Indikators auf der Menge der Zahlen in einer Zerlegungsstruktur umgesetzt wird. Dabei stellt man fest, daß die Adaptivität eine lokale Optimalitätseigenschaft bezüglich eines Maximum- oder Summenindikators ist. Es werden eindimensionale elliptische Randwertprobleme mit den bekannten Methoden und Lösungen geprüft, um die Region allgemeiner Ergebnisse zu demonstrieren und die adaptiven Übergangsoperatoren zu definieren.
Reviewer: H.F.Bauer

MSC:
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65J05 General theory of numerical analysis in abstract spaces
34B05 Linear boundary value problems for ordinary differential equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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