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In this paper, high-order numerical analysis of finite element method (FEM) is presented for two-dimensional multi-term time-fractional diffusion-wave equation (TFDWE). First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H 1−norm and temporal convergence in L 2-norm with order $$O(h^{2}+\tau^{3-\alpha})$$ O ( h 2 + τ 3 − α ) , where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H 1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Oct 4, 2018
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