Geodesic
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 3, pp. 455-484

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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.

DOI : 10.1051/m2an/2010009
Classification : 65N30, 65N15, 65N50, 65J15
Keywords: a posteriori error estimates, transition condition, parabolic problems 
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     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 },
     pages = {455--484},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     doi = {10.1051/m2an/2010009},
     mrnumber = {2666651},
     zbl = {1195.65117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010009/}
}
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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 , Tome 44 (2010) no. 3, pp. 455-484. doi: 10.1051/m2an/2010009

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