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Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data

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Abstract

This paper analyzes the convergence of a Petrov–Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established. Then an optimal convergence analysis with nonsmooth data is derived. Moreover, several numerical experiments are presented to validate the theoretical results.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Hao Luo, Binjie Li & Xiaoping Xie

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  1. Hao Luo
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  2. Binjie Li
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  3. Xiaoping Xie
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Correspondence to Binjie Li.

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This work was supported in part by National Natural Science Foundation of China (11771312).

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Luo, H., Li, B. & Xie, X. Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data. J Sci Comput 80, 957–992 (2019). https://doi.org/10.1007/s10915-019-00962-x

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  • DOI: https://doi.org/10.1007/s10915-019-00962-x

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