no. 6
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 991-1021

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, 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.

DOI : 10.1051/m2an:2006034
Classification : 65M60, 65M15, 65M50
Keywords: a posteriori error estimates, parabolic problems, discontinuous coefficients 
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     title = {Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients},
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Berrone, Stefano. Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 991-1021. doi: 10.1051/m2an:2006034

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