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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 -scheme with . 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 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...
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...
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