A posteriori error estimates for a nonconforming finite element discretization of the heat equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 2, p. 319-348

The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in d , d=2 or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results with minimal assumptions on the mesh. Numerical experiments and a space-time adaptive algorithm confirm the theoretical predictions.

DOI : https://doi.org/10.1051/m2an:2005009
Classification:  65N15,  65N30,  65M50
Keywords: error estimator, nonconforming FEM, heat equation
@article{M2AN_2005__39_2_319_0,
     author = {Nicaise, Serge and Soualem, Nadir},
     title = {A posteriori error estimates for a nonconforming finite element discretization of the heat equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {2},
     year = {2005},
     pages = {319-348},
     doi = {10.1051/m2an:2005009},
     zbl = {1078.65079},
     mrnumber = {2143951},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_2_319_0}
}
Nicaise, Serge; Soualem, Nadir. A posteriori error estimates for a nonconforming finite element discretization of the heat equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 2, pp. 319-348. doi : 10.1051/m2an:2005009. http://www.numdam.org/item/M2AN_2005__39_2_319_0/

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