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Stagnation in the p-version of the finite element method

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Abstract

A special feature of the p-version of the finite element method for solving a differential boundary value problem stated in the form of minimizing a quadratic functional on a certain set is studied. This special feature results in approximate solutions remaining unchanged on finite numbers of increasing finite-dimensional subsets of increasing dimension, in which solutions are sought. Necessary and sufficient conditions for the existence of this feature are found, and the stagnation effect is interpreted for a specially constructed example. For the adaptive p-version of the finite element approach, a modified strategy is proposed that takes this feature into account and thus improves the reliability of the method.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    N. D. Zolotareva & E. S. Nikolaev

Authors
  1. N. D. Zolotareva
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  2. E. S. Nikolaev
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Correspondence to N. D. Zolotareva.

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Original Russian Text © N.D. Zolotareva, E.S. Nikolaev, 2014, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2014, No. 3, pp. 5–13.

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Zolotareva, N.D., Nikolaev, E.S. Stagnation in the p-version of the finite element method. MoscowUniv.Comput.Math.Cybern. 38, 91–99 (2014). https://doi.org/10.3103/S0278641914030108

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  • DOI: https://doi.org/10.3103/S0278641914030108

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