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Error estimates for the numerical approximation of a quaslinear Neumann problem under minimal regularity of the data

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Abstract

The finite element based approximation of a quasilinear elliptic equation of non monotone type with Neumann boundary conditions is studied. Minimal regularity assumptions on the data are imposed. The consideration is restricted to polygonal domains of dimension two and polyhedral domains of dimension three. Finite elements of degree k ≥ 1 are used to approximate the equation. Error estimates are established in the L 2(Ω) and H 1(Ω) norms for convex and non-convex domains. The issue of uniqueness of a solution to the approximate discrete equation is also addressed.

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Authors and Affiliations

  1. Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecommunicación, Universidad de Cantabria, 39005, Santander, Spain

    Eduardo Casas

  2. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    Vili Dhamo

Authors
  1. Eduardo Casas
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  2. Vili Dhamo
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Correspondence to Eduardo Casas.

Additional information

E. Casas was partially supported by the Spanish Ministry of Science and Innovation under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010).

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Casas, E., Dhamo, V. Error estimates for the numerical approximation of a quaslinear Neumann problem under minimal regularity of the data. Numer. Math. 117, 115–145 (2011). https://doi.org/10.1007/s00211-010-0344-1

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