Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, p. 455-484

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.

DOI : https://doi.org/10.1051/m2an/2010009
Classification:  65N30,  65N15,  65N50,  65J15
Keywords: a posteriori error estimates, transition condition, parabolic problems
@article{M2AN_2010__44_3_455_0,
     author = {Berrone, Stefano},
     title = {Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     pages = {455-484},
     doi = {10.1051/m2an/2010009},
     zbl = {1195.65117},
     mrnumber = {2666651},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_3_455_0}
}
Berrone, Stefano. Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, pp. 455-484. doi : 10.1051/m2an/2010009. http://www.numdam.org/item/M2AN_2010__44_3_455_0/

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