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Techniques for Locally Adaptive Time Stepping Developed over the Last Two Decades

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

Adaptive mesh refinement techniques are well established and widely used for space discretizations. In contrast, local time stepping is much less used, and the corresponding techniques are less mature, needing delicate synchronization steps, which involve interpolation, extrapolation or projection. These operations can have adverse effects on the stability, and can also destroy important geometric properties of the scheme, like for example the conservation of invariants. We give here a survey on the intensive research performed in this direction over the last two decades.

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Author information

Authors and Affiliations

  1. University of Geneva, CH-1211, Geneva, Switzerland

    Martin J. Gander

  2. Université Paris 13, CNRS, UMR 7539 LAGA, 99 av. Jean-Baptiste Clément, 93430, 7 Villetaneuse, France

    Laurence Halpern

Authors
  1. Martin J. Gander
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  2. Laurence Halpern
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Correspondence to Martin J. Gander .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Gander, M.J., Halpern, L. (2013). Techniques for Locally Adaptive Time Stepping Developed over the Last Two Decades. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_44

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