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An improved a priori error analysis of Nitsche’s method for Robin boundary conditions

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Abstract

In a previous paper (Juntunen and Stenberg in Math Comput 78:1353–1374, 2009) we have extended Nitsche’s method (in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1970/71) for the Poisson equation with general Robin boundary conditions. The analysis required that the solution is in \(H^{s}\), with \(s>3/2\). Here we give an improved error analysis using a technique proposed by Gudi (Math Comput 79:2169–2189 2010).

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Authors and Affiliations

  1. Chair of Computational Science, ETH-Zentrum, Clausiusstrasse 33, CLT C 14, 8092, Zurich, Switzerland

    Nora Lüthen

  2. Kluuvintie 11 N, 02180, Espoo, Finland

    Mika Juntunen

  3. Department of Mathematics and Systems Analysis, Aalto University–School of Science, P.O. Box 11100, 00076, Espoo, Finland

    Rolf Stenberg

Authors
  1. Nora Lüthen
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  2. Mika Juntunen
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  3. Rolf Stenberg
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Correspondence to Rolf Stenberg.

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Lüthen, N., Juntunen, M. & Stenberg, R. An improved a priori error analysis of Nitsche’s method for Robin boundary conditions. Numer. Math. 138, 1011–1026 (2018). https://doi.org/10.1007/s00211-017-0927-1

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  • DOI: https://doi.org/10.1007/s00211-017-0927-1

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