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Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes

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  • Shi, Z.G.
  • Zhao, Y.M.
  • Liu, F.
  • Wang, F.L.
  • Tang, Y.F.

Abstract

The paper mainly focuses on studying nonconforming quasi-Wilson finite element fully-discrete approximation for two dimensional (2D) multi-term time fractional diffusion-wave equation (TFDWE) on regular and anisotropic meshes. Firstly, based on the Crank–Nicolson scheme in conjunction with L1-approximation of the time Caputo derivative of order α ∈ (1, 2), a fully-discrete scheme for 2D multi-term TFDWE is established. And then, the approximation scheme is rigorously proved to be unconditionally stable via processing fractional derivative skillfully. Moreover, the superclose result in broken H1-norm is deduced by utilizing special properties of quasi-Wilson element. In the meantime, the global superconvergence in broken H1-norm is derived by means of interpolation postprocessing technique. Finally, some numerical results illustrate the correctness of theoretical analysis on both regular and anisotropic meshes.

Suggested Citation

  • Shi, Z.G. & Zhao, Y.M. & Liu, F. & Wang, F.L. & Tang, Y.F., 2018. "Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 290-304.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:290-304
    DOI: 10.1016/j.amc.2018.06.026
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    References listed on IDEAS

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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    2. Yu, Bo & Jiang, Xiaoyun & Wang, Chu, 2016. "Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 106-118.
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