A Weak Galerkin Finite Element Method for Multi-Term Time-Fractional Diffusion Equations

The stability and convergence of a weak Galerkin finite element method for multi-term time-fractional diffusion equations with one-dimensional space variable are proved. Numerical experiments are consistent with theoretical analysis. AMS subject classifications: 65M12, 65M60

[1]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[2]  C. Lubich Discretized fractional calculus , 1986 .

[3]  M. Meerschaert,et al.  Numerical methods for solving the multi-term time-fractional wave-diffusion equation , 2012, Fractional calculus & applied analysis.

[4]  Jingjun Zhao,et al.  Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations , 2013 .

[5]  Bangti Jin,et al.  The Galerkin finite element method for a multi-term time-fractional diffusion equation , 2014, J. Comput. Phys..

[6]  Junping Wang,et al.  A computational study of the weak Galerkin method for second-order elliptic equations , 2011, Numerical Algorithms.

[7]  V. V. Gafiychuk,et al.  Pattern formation in a fractional reaction diffusion system , 2006 .

[8]  Tie Zhang,et al.  A weak Galerkin finite element method for Burgers' equation , 2016, J. Comput. Appl. Math..

[9]  Tie Zhang,et al.  A weak finite element method for elliptic problems in one space dimension , 2016, Appl. Math. Comput..

[10]  J. C. López-Marcos A difference scheme for a nonlinear partial integrodifferential equation , 1990 .

[11]  Shangyou Zhang,et al.  A Weak Galerkin Finite Element Method for the Maxwell Equations , 2013, Journal of Scientific Computing.

[12]  Lin Mu,et al.  A modified weak Galerkin finite element method for the Stokes equations , 2015, J. Comput. Appl. Math..

[13]  Francesco Mainardi,et al.  Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[14]  Yong Zhang,et al.  Particle tracking for fractional diffusion with two time scales , 2010, Comput. Math. Appl..

[15]  Chuanju Xu,et al.  Finite difference/spectral approximations for the time-fractional diffusion equation , 2007, J. Comput. Phys..

[16]  Junping Wang,et al.  Weak Galerkin finite element methods for Parabolic equations , 2012, 1212.3637.

[17]  Junping Wang,et al.  A weak Galerkin finite element method for second-order elliptic problems , 2011, J. Comput. Appl. Math..

[18]  C. Lubich Convolution quadrature and discretized operational calculus. I , 1988 .