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Calcolo Scientifico pp 373–433Cite as

Metodi numerici per problemi ai limiti stazionari ed evolutivi

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Part of the book series: UNITEXT ((UNITEXTMAT,volume 105))

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Questo capitolo tratta un caposaldo del Calcolo Scientifico, quello della risoluzione numerica di problemi ai limiti, stazionari e evolutivi. Introduciamo le classiche tecniche alle differenze finite, seguite da quelle basate sul metodo agli elementi finiti. Applichiamo questi metodi al caso dei problemi ai limiti ellitrtici, parabolici ed iperbolici. Ricordiamo i principali risultati di consistenza, stabilità, convergenza e indichiamo come affrontare la risoluzione numerica dei problemi algebrici corrispondenti. Vengono proposti svariati esempi, prima di concludere il capitolo con una robusta serie di esercizi.

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Notes

  1. 1.

    Si osservi che ora \(h\) indica il passo di discretizzazione spaziale (e non più il passo di discretizzazione temporale come fatto nel capitolo precedente).

  2. 2.

    L’analisi del metodo degli elementi finiti richiede strumenti analitici più raffinati che non intendiamo proporre in questo testo. Il lettore interessato può consultare, ad esempio, [Qua16, BS08, QV94].

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Author information

Authors and Affiliations

  1. École Polytechnique Fédérale (EPFL), Lausanne, Switzerland

    Alfio Quarteroni

  2. Politecnico di Milano, Milan, Italy

    Alfio Quarteroni

  3. MOX, Politecnico di Milano, Milan, Italy

    Fausto Saleri

  4. DICATAM, Università degli Studi di Brescia, Brescia, Italy

    Paola Gervasio

Authors
  1. Alfio Quarteroni
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  2. Fausto Saleri
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  3. Paola Gervasio
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Quarteroni, A., Saleri, F., Gervasio, P. (2017). Metodi numerici per problemi ai limiti stazionari ed evolutivi. In: Calcolo Scientifico. UNITEXT(), vol 105. Springer, Milano. https://doi.org/10.1007/978-88-470-3953-7_9

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