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Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

Author

Listed:
  • Jingjun Zhao
  • Jingyu Xiao
  • Yang Xu

Abstract

A finite element method (FEM) for multiterm fractional partial differential equations (MT‐FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT‐FPDEs and the existence and uniqueness of the weak solutions are obtained by the well‐known Lax‐Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT‐FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.

Suggested Citation

  • Jingjun Zhao & Jingyu Xiao & Yang Xu, 2013. "Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:857205
    DOI: 10.1155/2013/857205
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    References listed on IDEAS

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    1. T. E. Simos, 2012. "New Stable Closed Newton‐Cotes Trigonometrically Fitted Formulae for Long‐Time Integration," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Abdallah A. Badr, 2012. "Finite Element Method for Linear Multiterm Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Abdallah A. Badr, 2012. "Finite Element Method for Linear Multiterm Fractional Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, October.
    4. T. E. Simos, 2012. "New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, May.
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