On a method for a-posteriori error estimation of approximate solutions to parabolic problems

Juraj Weisz

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 4, page 735-740
  • ISSN: 0010-2628

Abstract

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The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.

How to cite

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Weisz, Juraj. "On a method for a-posteriori error estimation of approximate solutions to parabolic problems." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 735-740. <http://eudml.org/doc/247605>.

@article{Weisz1994,
abstract = {The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.},
author = {Weisz, Juraj},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {parabolic problem; a-posteriori error estimate; parabolic equation; Galerkin-Rothe method; orthogonal projection; a posteriori error estimates; dual problem; error bounds},
language = {eng},
number = {4},
pages = {735-740},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a method for a-posteriori error estimation of approximate solutions to parabolic problems},
url = {http://eudml.org/doc/247605},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Weisz, Juraj
TI - On a method for a-posteriori error estimation of approximate solutions to parabolic problems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 735
EP - 740
AB - The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.
LA - eng
KW - parabolic problem; a-posteriori error estimate; parabolic equation; Galerkin-Rothe method; orthogonal projection; a posteriori error estimates; dual problem; error bounds
UR - http://eudml.org/doc/247605
ER -

References

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  1. Eriksson K., Johnson C., Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. Numer. Anal. 28 (1991), 43-77. (1991) Zbl0732.65093MR1083324
  2. Gajewski H., Gröger K., Konjugierte Probleme und a-posteriori Fehlerabschätzungen,, Math. Nachrichten 73 (1976), 315-333. (1976) MR0435959
  3. Gajewski H., Gröger K., Zacharias K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie -Verlag Berlin, 1974 (Russian Mir Moskva 1978). MR0636412
  4. Weisz J., A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem, Commentationes Math. Univ. Carolinae 31 (1990), 315-322. (1990) Zbl0709.65074MR1077902

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