Brezzi, Franco and Hughes, Thomas J. R. and Süli, Endre:
Variational approximation of flux in conforming finite element methods for elliptic partial differential equations : a model problem (Approssimazione variazionale del flusso con elementi finiti conformi per problemi lineari ellittici : un problema modello)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 12 (2001), fasc. n.3, p. 159-166, (English)
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Si affronta il problema di approssimare il flusso del gradiente della soluzione di un problema ai limiti per una equazione lineare ellittica del secondo ordine, prendendo come problema modello il problema di Dirichlet per l’operatore di Laplace in due dimensioni spaziali. La linea $\Gamma$ lungo la quale si vuole approssimare il flusso è supposta essere rettilinea. L’approssimazione è costruita con elementi finiti continui e localmente polinomiali di grado $\le k$, con $k$ intero $\ge 1$. Tramite una opportuna definizione variazionale del flusso approsssimato, si ottengono stime dell’errore ottimali in spazi del tipo di $H^{-k-\frac{1}{2}} (\Gamma)$.
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