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

Published online by Cambridge University Press:  15 February 2007

Stefano Berrone
Stefano Berrone*
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. sberrone@calvino.polito.it
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Abstract

In this work we derive a posteriori error estimates basedon equations residuals for the heat equation with discontinuousdiffusivity coefficients. The estimates are based on a fully discretescheme based on conforming finite elements in each time slab andon 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 easyto identify a time-discretization error-estimatorand a space-discretization error-estimator. In this work we introduce a similarsplitting 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 boundswhose ratio is independent of any meshsize, timestep, problem parameter and its jumps.

Keywords

A posteriori error estimatesparabolic problemsdiscontinuous coefficients.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 6 , November 2006 , pp. 991 - 1021
Copyright
© EDP Sciences, SMAI, 2007

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