Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations

Stefano Berrone

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 3, page 455-484
  • ISSN: 0764-583X

Abstract

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In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time dependent problems.

How to cite

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Berrone, Stefano. "Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 455-484. <http://eudml.org/doc/250784>.

@article{Berrone2010,
abstract = { In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time dependent problems. },
author = {Berrone, Stefano},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {A posteriori error estimates; transition condition; parabolic problems; a posteriori error estimates; parabolic equations; theta method},
language = {eng},
month = {4},
number = {3},
pages = {455-484},
publisher = {EDP Sciences},
title = {Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations},
url = {http://eudml.org/doc/250784},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Berrone, Stefano
TI - Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 3
SP - 455
EP - 484
AB - In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time dependent problems.
LA - eng
KW - A posteriori error estimates; transition condition; parabolic problems; a posteriori error estimates; parabolic equations; theta method
UR - http://eudml.org/doc/250784
ER -

References

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