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INTERNODES for Elliptic Problems

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

The INTERNODES (INTERpolation for NOnconforming DEcompositionS) method is an interpolation based approach to solve partial differential equations on non-conforming discretizations. In this paper we sketch its formulation when it is applied to second-order elliptic problems. Therefore we apply it to the Kellogg’s test case with jumping coefficients and to an infinitely differentiable test solution. In both cases, INTERNODES attains optimal rate of convergence (i.e., that of the best approximation error in each subdomain).

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References

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Author information

Authors and Affiliations

  1. DICATAM, Università degli Studi di Brescia, Brescia, Italy

    Paola Gervasio

  2. MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy

    Alfio Quarteroni

  3. Institute of Mathematics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Alfio Quarteroni

Authors
  1. Paola Gervasio
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  2. Alfio Quarteroni
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Corresponding authors

Correspondence to Paola Gervasio or Alfio Quarteroni .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Gervasio, P., Quarteroni, A. (2018). INTERNODES for Elliptic Problems. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_32

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