## Abstract

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the L_{∞}(0, T; L_{2}(Ω)) norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the L_{∞}(0, T; L_{2}(Ω))-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Original language | English |
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Pages (from-to) | 1537-1569 |

Number of pages | 33 |

Journal | Mathematics of Computation |

Volume | 84 |

Issue number | 294 |

DOIs | |

Publication status | Published - 2015 |

### Bibliographical note

Publisher Copyright:© 2014 by the authors.

## ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

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