A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method

Ruan Zhousheng; Wang Zewen; Zhang Wen

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A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method

机译：基于有限元方法的时间分数维扩散方程的直接数值算法

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We study a backward problem for a time-fractional diffusion equation, which is formulated into a regularized optimization problem. After solving a sequence of well-posed direct problems by the finite element method, a directly numerical algorithm is proposed for solving the regularized optimization problem. In order to obtain a reasonable regularization solution, we utilize the discrepancy principle with decreasing geometric sequence to choose regularization parameters. One- and two-dimensional examples are given to verify the efficiency and stability of the proposed method.

机译：我们研究了时间分数阶扩散方程的后向问题，该方程被公式化为正则化优化问题。在利用有限元方法解决了一系列正定的直接问题之后，提出了一种直接数值算法来求解正则化优化问题。为了获得合理的正则化解决方案，我们利用几何序列递减的差异原理来选择正则化参数。给出了一个一维和二维示例来验证所提出方法的效率和稳定性。

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《Mathematical Problems in Engineering》 |2015年第5期|414727.1-414727.8|共8页
作者
Ruan Zhousheng; Wang Zewen; Zhang Wen;
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Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China.;

E China Inst Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China.;

E China Inst Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China.;

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8. An Investigation of the Numerical Methods of Finite Differences and Finite Elements for Digital Computer Solution of the Transient Heat Conduction (Diffusion) Equation Using Optimum Implicit Formulations. [R] . martin,charles r. 1978

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A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method

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