FEM for time-fractional diffusion equations, novel optimal error analyses

Preprint English OPEN
Mustapha, Kassem;
(2016)
  • Subject: Mathematics - Numerical Analysis

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to both the convergenc... View more
  • References (23)
    23 references, page 1 of 3

    [1] A. Alikhanov, A new difference scheme for the time fractional diffusion equation, J. Comput. Phys., 280 (2013), 424-438

    [2] H. Brunner, L. Ling and M. Yamamoto, Numerical simulations of 2D fractional subdiffusion problems, J. Comput. Phys., 229 (2010), 6613-6622

    [3] J. Chen, F. Liu, Q. Liu, X. Chen, V. Anh, I. Turner and K. Burrage, Numerical simulation for the three-dimension fractional sub-diffusion equation, Appl. Math. Model., 38 (2014), 3695-3705

    [4] M. Cui, Compact alternating direction implicit method for two-dimensional time fractional diffusion equation, J. Comput. Phys., 231 (2012), 2621-2633

    [5] B. Jin, R. Lazarov and Z. Zhou, Error estimates for a semidiscrete finite element method for fractional order parabolic equations, SIAM J. Numer. Anal., 51 (2013), 445-466

    [6] B. Jin, R. Lazarov, J. Pascal and Z. Zhou, Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion, IMA J. Numer. Anal., 35 (2015), 561- 582

    [7] S. Karaa, K. Mustapha and A. K. Pani, A priori estimates of a finite element method for fractional diffusion problems by energy arguments, SIAM J. Numer. Anal., (2016)

    [8] K. N. Le, W. McLean and K. Mustapha, Numerical solution of the time-fractional FokkerPlanck equation with general forcing, SIAM J. Numer. Anal., 54, 1763-1784

    [9] X. Li and C. Xu, A Space-Time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal., 47 (2009), 2108-2131

    [10] Y. Lin, and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225 (2007), 1533-1552

  • Metrics
Share - Bookmark