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A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

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Summary

Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP th-degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.

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Authors and Affiliations

  1. Institut de Mathematiques, Université des Sciences et de la Technologie Houari Boumèdiene, El-Alia BP No. 32, Bab Ezzouar Alger, Algeria

    Slimane Adjerid

  2. Department of Computer Science and Scientific Computation Research Center, Rensselaer Polytechnic Institute, 12180-3590, Troy., NY, USA

    Joseph E. Flaherty & Yun J. Wang

Authors
  1. Slimane Adjerid
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  2. Joseph E. Flaherty
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  3. Yun J. Wang
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Additional information

This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910

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Adjerid, S., Flaherty, J.E. & Wang, Y.J. A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. Numer. Math. 65, 1–21 (1993). https://doi.org/10.1007/BF01385737

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  • DOI: https://doi.org/10.1007/BF01385737

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