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Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order

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Summary

For second order linear elliptic problems, it is proved that theP 1-nonconforming finite element method has the sameL ∞-asymptotic accuracy as theP 1-conforming one. This result is applied to derive optimalL ∞-error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Pavia, Italy

    Lucia Gastaldi

  2. Programa Especial de Matemática Aplicada, Instituto de Desarrollo Tecnológico para la Industria Quimica, Santa Fe, Argentina

    Ricardo Nochetto

  3. Istituto di Analisi Numerica del C.N.R., Pavia, Italy

    Ricardo Nochetto

Authors
  1. Lucia Gastaldi
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  2. Ricardo Nochetto
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Additional information

Performed in the research program of Istituto di Analisi Numerica of C.N.R. of Pavia

Partially supported by MPI, GNIM of CNR, Italy

Supported by “Consejo Nacional de Investigaciones Cientificas y Técnicas”, Argentina

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Gastaldi, L., Nochetto, R. Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order. Numer. Math. 50, 587–611 (1987). https://doi.org/10.1007/BF01408578

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