ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations

Berrone, Stefano

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.


In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-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 problems.

(Received April 15 2008)

(Revised July 28 2009)

(Online publication February 4 2010)

Key Words:

  • A posteriori error estimates;
  • transition condition;
  • parabolic problems

Mathematics Subject Classification:

  • 65N30;
  • 65N15;
  • 65N50;
  • 65J15