Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation
Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation
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DOI：
10.1007/s10915-017-0385-z
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发表时间：
2017-02
影响因子：
2.5
通讯作者：
Jincheng Ren;Xiaonian Long;S. Mao;Jiwei Zhang
中科院分区：
文献类型：
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作者：
Jincheng Ren;Xiaonian Long;S. Mao;Jiwei Zhang
本文讨论了时间分数阶扩散-波动方程全离散有限元逼近的误差估计。基于空间离散的标准Galerkin有限元方法和时间分数阶导数近似的L1公式，得到了求解常系数分数阶扩散-波动方程的全离散格式，并给出并分析了超收敛估计。在此基础上，给出了求解变系数分数阶扩散波动方程的全离散有限元格式，并给出了相应的误差估计。最后，通过数值实验对理论结果进行了验证。
In this paper, the error estimates of fully discrete finite element approximation for the time fractional diffusion-wave equation are discussed. Based on the standard Galerkin finite element method approach for the spatial discretization and theL1 formula for the approximation of the time fractional derivative, the fully discrete scheme for solving the constant coefficient fractional diffusion-wave equation is obtained and the superconvergence estimate is proposed and analyzed. Further, a fully discrete finite element scheme is presented for solving the variable coefficient fractional diffusion-wave equation and the corresponding error estimates are also established. Finally, numerical experiments are included to support the theoretical results.