A NOVEL FINITE ELEMENT METHOD FOR A CLASS OF TIME FRACTIONAL DIFFUSION EQUATIONS

被引:0
作者
Sun, H. G. [1 ]
Chen, W.
Sze, K. Y. [1 ]
机构
[1] Univ Hong Kong, Dept Mech Engn, Pokfulam, Hong Kong, Peoples R China
来源
PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2011, VOL 3, PTS A AND B | 2012年
关键词
ADVECTION-DISPERSION EQUATION; ANOMALOUS DIFFUSION; DIFFERENTIAL-EQUATIONS; SOLUTE TRANSPORT; SPACE; APPROXIMATION; BOUNDARY; MEDIA;
D O I
暂无
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Anomalous transport of contaminants in groundwater or porous soil is a research focus in hydrology and soil science for decades. Because fractional diffusion equations can well characterize early breakthrough and heavy tail decay features of contaminant transport process, they have been considered as promising tools to simulate anomalous transport processes in complex media. However, the efficient and accurate computation of fractional diffusion equations is a main task in their applications. In this paper, we introduce a novel numerical method which captures the critical Mittag-Leffler decay feature of subdiffusion in time direction, to solve a class of time fractional diffusion equations. A key advantage of the new method is that it overcomes the critical problem in the application of time fractional differential equations: long-time range computation. To illustrate its efficiency and simplicity, three typical academic examples are presented. Numerical results show a good agreement with the exact solutions.
引用
收藏
页码:369 / 376
页数:8
相关论文
共 50 条
  • [21] Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
    Bu, Weiping
    Tang, Yifa
    Wu, Yingchuan
    Yang, Jiye
    JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 264 - 279
  • [22] An adaptive finite element method for the sparse optimal control of fractional diffusion
    Otarola, Enrique
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (02) : 302 - 328
  • [23] Leapfrog/Finite Element Method for Fractional Diffusion Equation
    Zhao, Zhengang
    Zheng, Yunying
    SCIENTIFIC WORLD JOURNAL, 2014,
  • [24] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
    Bu, Weiping
    Tang, Yifa
    Yang, Jiye
    JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 276 : 26 - 38
  • [25] A novel approach of high accuracy analysis of anisotropic bilinear finite element for time-fractional diffusion equations with variable coefficient
    Wang, F. L.
    Liu, F.
    Zhao, Y. M.
    Shi, Y. H.
    Shi, Z. G.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (10) : 3786 - 3800
  • [26] Error estimates of a semidiscrete finite element method for fractional stochastic diffusion-wave equations
    Zou, Guang-an
    Atangana, Abdon
    Zhou, Yong
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (05) : 1834 - 1848
  • [27] Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations
    Ma, Jingtang
    Zhou, Zhiqiang
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2016, 8 (06) : 911 - 931
  • [28] A MIXED FINITE ELEMENT METHOD FOR NONLINEAR DIFFUSION EQUATIONS
    Burger, Martin
    Carrillo, Jose A.
    Wolfram, Marie-Therese
    KINETIC AND RELATED MODELS, 2010, 3 (01) : 59 - 83
  • [29] The time discontinuous space-time finite element method for fractional diffusion-wave equation
    Zheng, Yunying
    Zhao, Zhengang
    APPLIED NUMERICAL MATHEMATICS, 2020, 150 (150) : 105 - 116
  • [30] Adaptive finite element method for fractional differential equations using hierarchical matrices
    Zhao, Xuan
    Hu, Xiaozhe
    Cai, Wei
    Karniadakis, George Em
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 325 : 56 - 76