Finite Elemente Und Differenzenverfahren: Spezialtagung Über «Finite Elemente Und Differenzenverfahren» Vom 25. Bis 27. September 1974 an Der Technisc
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Der vorliegende Band gibt haupts�chlich Vortr�ge wieder, die in der Zeit vom 25. bis 27. September 1974 auf einem an der Technischen Universit�t Claus- thai abgehaltenen, von den Unterzeichneten geleiteten Kolloquium �ber Finite Elemente und Differenzenverfahrem> gehalten wurden. Diese beiden Methoden sind wohl die z. Z. am meisten verwendeten numerischen N�herungsverfahren zur angen�herten L�sung von Anfangs- und Randwertaufgaben bei gew�hnlichen und partiellen, linearen und nichtli- nearen Differentialgleichungen. Die im Laufe der letzten 2 bis 2Y2 Jahrzehnte entwickelte Methode der finiten Elemente hat wegen ihrer gro en Flexibilit�t und Anwendbarkeit auch bei sehr komplizierten Aufgaben besonders in den Anwendungsgebieten gro en Anklang gefunden, und es werden z. B. bei Problemen der Kontinuumsmechanik auf Computern Probleme mit �ber 10 000 nichtlinearen Gleichungen numerisch bew�ltigt. Trotz der au eror- dentlichen praktischen Erfolge sind erst in neuerer Zeit von mathematischer Seite aus Versuche unternommen worden, eine strenge Fehleranalyse durch- zuf�hren; exakte Fehlerschranken f�r die auf dem Computer berechneten N�herungen lassen sich z. Z. nur f�r relativ einfache Probleme angeben. Einige der Vortr�ge berichten �ber derartige M�glichkeiten, deren weiterer Ausbau als wichtige Aufgabe f�r k�nftige mathematische Forschung erscheint, andere Vortr�ge �ber Weiterentwicklungen numerischer Methoden, �ber Konvergenzordnungen und �ber Vergleiche verschiedener Verfahren miteinander. Das Ziel der Tagung war, dazu beizutragen, die z. Z. auf dem Gebiete der numerischen Behandlung von Differentialgleichungen bestehende Diskrepanz zwischen Theorie und Praxis ein wenig zu verringern.
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