# Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation

- Volume: 13, Issue: 2, page 121-133
- ISSN: 1120-6330

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topRepin, 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 13.2 (2002): 121-133. <http://eudml.org/doc/252364>.

@article{Repin2002,

abstract = {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]).},

author = {Repin, Sergey},

journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},

keywords = {Parabolic equations; Deviations from exact solution; A posteriori estimates; parabolic equations; deviations from exact solution; a posteriori estimates},

language = {eng},

month = {6},

number = {2},

pages = {121-133},

publisher = {Accademia Nazionale dei Lincei},

title = {Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation},

url = {http://eudml.org/doc/252364},

volume = {13},

year = {2002},

}

TY - JOUR

AU - Repin, Sergey

TI - Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation

JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

DA - 2002/6//

PB - Accademia Nazionale dei Lincei

VL - 13

IS - 2

SP - 121

EP - 133

AB - 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]).

LA - eng

KW - Parabolic equations; Deviations from exact solution; A posteriori estimates; parabolic equations; deviations from exact solution; a posteriori estimates

UR - http://eudml.org/doc/252364

ER -

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