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Error Estimates for the Coupling of Analytical and Numerical Solutions

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Abstract

In this paper we present error estimates for a continuous coupling of an analytical and a numerical solution for a boundary value problem with a singularity. A solution of the Lamé–Navier equation with a singularity caused by a crack is considered as an example. The analytical solution near a singularity is constructed by using complex function theory and coupled continuously with the finite element solution. The objective of this paper is to estimate the coupling error, which cannot be covered by the classical theory of the finite element method.

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Acknowledgments

The research of U. Kähler is supported by Portuguese funds through the CIDMA, Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The research of D. Legatiuk is supported by the German Research Foundation (DFG) via Research Training Group “Evaluation of Coupled Numerical Partial Models in Structural Engineering (GRK 1462)”, which is gratefully acknowledged.

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Authors and Affiliations

  1. Bauhaus-Universität Weimar, 99423, Weimar, Germany

    Klaus Gürlebeck

  2. CIDMA, Center for R&D in Mathematics and Applications, Universidade de Aveiro, Aveiro, Portugal

    Uwe Kähler

  3. Research Training Group 1462, Bauhaus-Universität Weimar, 99425, Weimar, Germany

    Dmitrii Legatiuk

Authors
  1. Klaus Gürlebeck
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  2. Uwe Kähler
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  3. Dmitrii Legatiuk
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Corresponding author

Correspondence to Dmitrii Legatiuk.

Additional information

Communicated by Fabrizio Colombo.

Dedicated to Frank Sommen on the occasion of his 60th birthday.

The research of U. Kähler is supported by Portuguese funds through the CIDMA, Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The research of D. Legatiuk is supported by the German Research Foundation (DFG) via Research Training Group “Evaluation of Coupled Numerical Partial Models in Structural Engineering (GRK 1462)”, which is gratefully acknowledged.

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Gürlebeck, K., Kähler, U. & Legatiuk, D. Error Estimates for the Coupling of Analytical and Numerical Solutions. Complex Anal. Oper. Theory 11, 1221–1240 (2017). https://doi.org/10.1007/s11785-016-0583-y

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  • DOI: https://doi.org/10.1007/s11785-016-0583-y

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