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

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- 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 40.6 (2007): 991-1021. <http://eudml.org/doc/194348>.

@article{Berrone2007,

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 θ-scheme with 1/2 ≤ θ ≤ 1.
Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo40 (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},

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

language = {eng},

month = {2},

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/194348},

volume = {40},

year = {2007},

}

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

DA - 2007/2//

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 θ-scheme with 1/2 ≤ θ ≤ 1.
Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo40 (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.; a posteriori error estimates; finite elements; discontinuous coefficients; heat equation

UR - http://eudml.org/doc/194348

ER -

## References

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