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...

In this work we derive 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 -scheme with 1/2 ≤ ≤ 1.
Following remarks of [Picasso, . (1998) 223–237; Verfürth,
(2003) 195–212] it is easy
to identify a time-discretization error-estimator
and a space-discretization error-estimator. In this work we...

In this paper we derive error estimates for the
heat equation. The time discretization
strategy is based on a -method and the mesh used for each
time-slab is independent of the mesh used for the previous
time-slab. The novelty of this paper is an upper bound for the
error caused by the coarsening of the mesh used for computing the
solution in the previous time-slab. The technique applied for
deriving this upper bound is independent of the problem and can be
generalized to other time dependent...

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