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In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable -scheme with . Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223-237; Verfürth, Calcolo 40 (2003) 195-212] it is easy to identify a time-discretization error-estimator and a space-discretization error-estimator. In this work we introduce a similar splitting for the data-approximation error in time and in space. Assuming the quasi-monotonicity condition [Dryja et al., Numer. Math. 72 (1996) 313-348; Petzoldt, Adv. Comput. Math. 16 (2002) 47-75] we have upper and lower bounds whose ratio is independent of any meshsize, timestep, problem parameter and its jumps.
@article{M2AN_2006__40_6_991_0,
author = {Berrone, Stefano},
title = {Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {991--1021},
publisher = {EDP-Sciences},
volume = {40},
number = {6},
year = {2006},
doi = {10.1051/m2an:2006034},
mrnumber = {2297102},
zbl = {1121.65098},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006034/}
}
TY - JOUR AU - Berrone, Stefano TI - Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2006 SP - 991 EP - 1021 VL - 40 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006034/ DO - 10.1051/m2an:2006034 LA - en ID - M2AN_2006__40_6_991_0 ER -
%0 Journal Article %A Berrone, Stefano %T Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2006 %P 991-1021 %V 40 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006034/ %R 10.1051/m2an:2006034 %G en %F M2AN_2006__40_6_991_0
Berrone, Stefano. Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 991-1021. doi: 10.1051/m2an:2006034
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