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A posteriori error estimates for mixed finite element approximations of parabolic problems

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Abstract

We derive residual based a posteriori error estimates for parabolic problems on mixed form solved using Raviart–Thomas–Nedelec finite elements in space and backward Euler in time. The error norm considered is the flux part of the energy, i.e. weighted L 2(Ω) norm integrated over time. In order to get an optimal order bound, an elementwise computable post-processed approximation of the scalar variable needs to be used. This is a common technique used for elliptic problems. The final bound consists of terms, capturing the spatial discretization error and the time discretization error and can be used to drive an adaptive algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Umeå University, Umeå, Sweden

    Mats G. Larson

  2. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Axel Målqvist

Authors
  1. Mats G. Larson
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  2. Axel Målqvist
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Correspondence to Axel Målqvist.

Additional information

A. Målqvist’s work is supported by The Göran Gustafsson Foundation.

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Larson, M.G., Målqvist, A. A posteriori error estimates for mixed finite element approximations of parabolic problems. Numer. Math. 118, 33–48 (2011). https://doi.org/10.1007/s00211-010-0328-1

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  • DOI: https://doi.org/10.1007/s00211-010-0328-1

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