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; Verf¨urth, 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.

Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients / Berrone, Stefano. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - STAMPA. - 40:6(2006), pp. 991-1021.

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

BERRONE, Stefano
2006

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; Verf¨urth, 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1634939
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