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The finite element method for parabolic equations

II. A posteriori error estimation and adaptive approach

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Summary

We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.

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Authors and Affiliations

  1. Laboratory of Applied Studies, Division of Computer Research and Technology, National Institutes of Health, 20205, Bethesda, MD, USA

    M. Bieterman

  2. Institute for Physical Science and Technology, and Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    I. Babuška

Authors
  1. M. Bieterman
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  2. I. Babuška
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Additional information

The work was partially supported by ONR Contract N00014-77-C-0623

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Bieterman, M., Babuška, I. The finite element method for parabolic equations. Numer. Math. 40, 373–406 (1982). https://doi.org/10.1007/BF01396452

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  • DOI: https://doi.org/10.1007/BF01396452

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