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A space-time finite element method for solving linear Riesz space fractional partial differential equations

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Abstract

In this paper, numerical solutions for linear Riesz space fractional partial differential equations with a second-order time derivative are considered. A space-time finite element method is proposed to solve these equations numerically. In the time direction, the C0-continuous Galerkin method is used to approximate the second-order time derivative. In the space direction, the usual linear finite element method is developed to approximate the space fractional derivative. The matrix equivalent form of this numerical method is deduced. The stability of the discrete solution is established and the optimal error estimates are investigated. Some numerical tests are given to validate the theoretical results.

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Funding

The work of J. Lai was supported by Natural Science Foundation of Fujian Province of China (2016J01670) and was carried out while J. Lai was a visiting scholar (funded by Minjiang University) at Queensland University of Technology. The authors wish to acknowledge that this research was partially supported by the Australian Research Council via the Discovery Projects DP180103858 and DP190101889, and National Natural Science Foundation of China (No. 11771364).

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Authors and Affiliations

  1. College of Mathematics and Data Science, Minjiang University, Fuzhou, 350108, People’s Republic of China

    Junjiang Lai

  2. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

    Fawang Liu

  3. Faculty of Science, Engineering and Technology, Swinburne University of Technology, PO Box 218, Hawthorn, VIC, 3122, Australia

    Vo V. Anh

  4. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Qingxia Liu

Authors
  1. Junjiang Lai
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  2. Fawang Liu
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  3. Vo V. Anh
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  4. Qingxia Liu
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Correspondence to Fawang Liu.

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Lai, J., Liu, F., Anh, V.V. et al. A space-time finite element method for solving linear Riesz space fractional partial differential equations. Numer Algor 88, 499–520 (2021). https://doi.org/10.1007/s11075-020-01047-9

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  • DOI: https://doi.org/10.1007/s11075-020-01047-9

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