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A note on the H 1-convergence of the overlapping Schwarz waveform relaxation method for the heat equation

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Abstract

The overlapping Schwarz waveform relaxation method is a parallel iterative method for solving time-dependent PDEs. Convergence of the method for the linear heat equation has been studied under infinity norm but it was unknown under the energy norm at the continuous level. The question is interesting for applications concerning fluxes or gradients of the solutions. In this work, we show that the energy norm of the errors of iterates is bounded by their infinity norm. Therefore, we give an affirmative answer to this question for the first time.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Hui Zhang & Yao-Lin Jiang

  2. Department of Mathematics, University of Geneva, Geneve, 1211, Switzerland

    Hui Zhang

Authors
  1. Hui Zhang
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  2. Yao-Lin Jiang
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Correspondence to Yao-Lin Jiang.

Additional information

The work was supported by the Natural Science Foundation of China (11071192) and the International Science and Technology Cooperation Program of China (2010DFA14700).

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Zhang, H., Jiang, YL. A note on the H 1-convergence of the overlapping Schwarz waveform relaxation method for the heat equation. Numer Algor 66, 299–307 (2014). https://doi.org/10.1007/s11075-013-9734-7

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  • DOI: https://doi.org/10.1007/s11075-013-9734-7

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