On Density and Approximation Properties of Special Solutions of the Helmohltz Equation
Identifieur interne : 001097 ( Istex/Corpus ); précédent : 001096; suivant : 001098On Density and Approximation Properties of Special Solutions of the Helmohltz Equation
Auteurs : Dominik StillSource :
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik [ 0044-2267 ] ; 1992.
Abstract
We consider eigenvalue problems for the Laplace operator on a region G. Especially if G is simply‐shaped, defect‐minimization methods with trial functions φ satisfying the Helmholtz equation Δφ + λφ = 0 may be suitable for the numerical solution of the problem. Such functions φ are given for example by the classical method of separation of variables. This paper is concerned with density and approximation properties of these special solutions of the Helmholtz equation with respect to the supremum‐norm.
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DOI: 10.1002/zamm.19920720711
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Especially if G is simply‐shaped, defect‐minimization methods with trial functions φ satisfying the Helmholtz equation Δφ + λφ = 0 may be suitable for the numerical solution of the problem. Such functions φ are given for example by the classical method of separation of variables. This paper is concerned with density and approximation properties of these special solutions of the Helmholtz equation with respect to the supremum‐norm.</abstract><abstract lang="de">Wir betrachten Eigenwertprobleme für den Laplace‐Operator auf einem Gebiet G. Insbesondere wenn G einfache Form hat, können Defekt‐Minimierungsmethoden mit Testfunktionen φ die die Helmholtz‐Gleichung Δφ + λφ = 0 erfüllen, zur numerischen Lösung ds problems geeignet sein. Solche Funktionen φ werden zum Beispiel durch die klassische Methode der Variablentrennung gegeben. 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