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Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation

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  • An, Na
  • Huang, Chaobao
  • Yu, Xijun

Abstract

Based on the finite difference scheme in temporal and the direct discontinuous Galerkin (DDG) method in spatial, a fully discrete DDG scheme is first proposed to solve the two-dimensional fractional diffusion-wave equation with Caputo derivative of order 1 < α < 2. The proposed scheme is unconditional stable, and the spatial global convergence and the temporal convergence order of O(Δt+hk+1) is derived in L2 norm with Pk polynomial. Numerical experiments are presented to demonstrate the theoretical results.

Suggested Citation

  • An, Na & Huang, Chaobao & Yu, Xijun, 2019. "Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 148-157.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:148-157
    DOI: 10.1016/j.amc.2018.12.048
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    References listed on IDEAS

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    1. Wei, Leilei, 2017. "Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 180-189.
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    Cited by:

    1. Yan, Xiong-bin & Zhang, Zheng-qiang & Wei, Ting, 2022. "Simultaneous inversion of a time-dependent potential coefficient and a time source term in a time fractional diffusion-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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