Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation
Repin, Sergey
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002), p. 121-133 / Harvested from Biblioteca Digitale Italiana di Matematica
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The paper is concerned with deriving functionals that give upper bounds of the difference between the exact solution of the initial-boundary value problem for the heat equation and any admissible function from the functional class naturally associated with this problem. These bounds are given by nonegative functionals called deviation majorants, which vanish only if the function and exact solution coincide. The deviation majorants pose a new type of a posteriori estimates that can be used in numerical analysis. Also, the estimates formed by such majorants can be viewed as a certain extension of well known «energy» estimates for solutions of parabolic type problems (see [1]).

Questa Nota è rivolta allo studio di funzionali che stabiliscono limiti superiori per la differenza tra soluzioni esatte del problema di Cauchy-Dirichlet per l’equazione del calore e qualsiasi funzione ammissibile nella classe associata in modo naturale a questo problema. Tali limiti sono espressi da funzionali non negativi, detti maggioranti di deviazione, che si annullano solo se la funzione coincide con la soluzione esatta. I maggioranti di deviazione pongono un nuovo tipo di stime a posteriori che possono essere utili nell’analisi numerica. Le stime date da questi maggioranti possono inoltre essere considerate come prolungamenti di stime dell’energia ben note per la soluzione di problemi di tipo parabolico (vedi [1]).

Publié le : 2002-06-01
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     author = {Sergey Repin},
     title = {Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {13},
     year = {2002},
     pages = {121-133},
     zbl = {1221.65244},
     mrnumber = {1949485},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_2_121_0}
}

Repin, Sergey. Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002) pp. 121-133. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_2_121_0/

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