# Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients

- Volume: 40, Issue: 6, page 991-1021
- ISSN: 0764-583X

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topBerrone, Stefano. "Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 40.6 (2006): 991-1021. <http://eudml.org/doc/244686>.

@article{Berrone2006,

abstract = {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 $\theta $-scheme with $1/2\le \theta \le 1$. 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.},

author = {Berrone, Stefano},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {a posteriori error estimates; parabolic problems; discontinuous coefficients; finite elements; heat equation},

language = {eng},

number = {6},

pages = {991-1021},

publisher = {EDP-Sciences},

title = {Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients},

url = {http://eudml.org/doc/244686},

volume = {40},

year = {2006},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2006

PB - EDP-Sciences

VL - 40

IS - 6

SP - 991

EP - 1021

AB - 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 $\theta $-scheme with $1/2\le \theta \le 1$. 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.

LA - eng

KW - a posteriori error estimates; parabolic problems; discontinuous coefficients; finite elements; heat equation

UR - http://eudml.org/doc/244686

ER -

## References

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