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Analysis of the combined finite element and Fourier interpolation

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Summary

We consider Lagrange interpolation involving trigonometric polynomials of degree ≦N in one space direction, and piecewise polynomials over a finite element decomposition of mesh size ≦h in the other space directions. We provide error estimates in non-isotropic Sobolev norms, depending additively on the parametersh andN. An application to the convergence analysis of an elliptic problem, with some numerical results, is given.

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Authors and Affiliations

  1. Istituto di Matematica Applicata, Università di Pavia, 27100, Pavia, Italy

    C. Canuto

  2. Analyse Numérique, T. 55-65, Université P. & M. Curie, 4 Place Jussieu, 75230, Paris Cedex 05, France

    Y. Maday

  3. Istituto di Analisi Numerica del C.N.R., C. so C. Alberto, 5, 27100, Pavia, Italy

    A. Quarteroni

Authors
  1. C. Canuto
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  2. Y. Maday
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  3. A. Quarteroni
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Canuto, C., Maday, Y. & Quarteroni, A. Analysis of the combined finite element and Fourier interpolation. Numer. Math. 39, 205–220 (1982). https://doi.org/10.1007/BF01408694

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