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On mixed finite element methods for first order elliptic systems

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Summary

A physically based duality theory for first order elliptic systems is shown to be of central importance in connection with the Galerkin finite element solution of these systems. Using this theory in conjunction with a certain hypothesis concerning approximation spaces, optimal error estimates for Galerkin type approximations are demonstrated. An example of a grid which satisfies the hypothesis is given and numerical examples which illustrate the theory are provided.

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Authors and Affiliations

  1. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, Pennsylvania, USA

    G. J. Fix

  2. Department of Mathematics, University of Tennessee, 37916, Knoxville, Tennessee, USA

    M. D. Gunzburger

  3. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, Pennsylvania, USA

    R. A. Nicolaides

Authors
  1. G. J. Fix
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  2. M. D. Gunzburger
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  3. R. A. Nicolaides
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Fix, G.J., Gunzburger, M.D. & Nicolaides, R.A. On mixed finite element methods for first order elliptic systems. Numer. Math. 37, 29–48 (1981). https://doi.org/10.1007/BF01396185

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  • DOI: https://doi.org/10.1007/BF01396185

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