The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in , 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.
Mots clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {319--348},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/m2an:2005009},
mrnumber = {2143951},
zbl = {1078.65079},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005009/}
}
TY - JOUR AU - Nicaise, Serge AU - Soualem, Nadir TI - A posteriori error estimates for a nonconforming finite element discretization of the heat equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 319 EP - 348 VL - 39 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005009/ DO - 10.1051/m2an:2005009 LA - en ID - M2AN_2005__39_2_319_0 ER -
%0 Journal Article %A Nicaise, Serge %A Soualem, Nadir %T A posteriori error estimates for a nonconforming finite element discretization of the heat equation %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 319-348 %V 39 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005009/ %R 10.1051/m2an:2005009 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 319-348. doi : 10.1051/m2an:2005009. http://www.numdam.org/articles/10.1051/m2an:2005009/
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