Geodesic
Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 121-133

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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]). 
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     author = {Repin, Sergey},
     title = {Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {121--133},
     publisher = {mathdoc},
     volume = {Ser. 9, 13},
     number = {2},
     year = {2002},
     zbl = {1221.65244},
     mrnumber = {MR1949485},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a6/}
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Repin, Sergey. Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 121-133. http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a6/