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SCIENTIA SINICA Informationis, Volume 48, Issue 7: 871-887(2018) https://doi.org/10.1360/N112017-00295

High-accuracy analysis of finite-element method for two-term mixed time-fractional diffusion-wave equations

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  • ReceivedMar 27, 2018
  • AcceptedApr 8, 2018
  • PublishedJul 12, 2018

Abstract

Based on the finite-element method (FEM) in the spatial direction and L1-CN approximation in the temporal direction, respectively, numerical analyses are proposed for 2D two-term mixed time-fractional diffusion-wave equations. First, a fully discrete approximate scheme is established for the equation, and it is proved to be unconditionally stable. Then, rigorous proofs are provided for the convergence result in the $L^2$- norm and superclose properties in $H^1$- norm with order $~O(h^2+\displaystyle\tau^{\min\{2-\alpha_1,~3-\alpha\}})~~(0<\alpha_1<1,1<\alpha<2)$, where $h$ and $~\tau~$ are the spatial size and time step, respectively. Furthermore, the global superconvergence in the $H^1$- norm is obtained using an interpolation postprocessing technique. Finally, with the help of numerical examples, the correctness and high efficiency of the theoretical analysis are further demonstrated.


Funded by

国家自然科学基金(11771438)


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