Superconvergence analysis of a new low order nonconforming MFEM for time-fractional diffusion equation

[1]  R. Rannacher,et al.  Simple nonconforming quadrilateral Stokes element , 1992 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.

[4]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[5]  Lutz Tobiska,et al.  The streamline–diffusion method for nonconforming Qrot1 elements on rectangular tensor–product meshes , 2001 .

[6]  Dongwoo Sheen,et al.  P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems , 2003, SIAM J. Numer. Anal..

[7]  J. Klafter,et al.  The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics , 2004 .

[8]  Shi,et al.  CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT , 2005 .

[9]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[10]  Santanu Saha Ray,et al.  Analytical solution of a fractional diffusion equation by Adomian decomposition method , 2006, Appl. Math. Comput..

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

[12]  Fawang Liu,et al.  Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation , 2007, Appl. Math. Comput..

[13]  Ningning Yan,et al.  Superconvergence analysis of the nonconforming quadrilateral linear-constant scheme for Stokes equations , 2008, Adv. Comput. Math..

[14]  S. Das,et al.  Analytical solution of a fractional diffusion equation by variational iteration method , 2009, Comput. Math. Appl..

[15]  Feng Shi,et al.  A new stabilized mixed finite-element method for Poisson equation based on two local Gauss integrations for linear element pair , 2011, Int. J. Comput. Math..

[16]  Yadong Zhang,et al.  High accuracy analysis of a new nonconforming mixed finite element scheme for Sobolev equations , 2011, Appl. Math. Comput..

[17]  Jingtang Ma,et al.  High-order finite element methods for time-fractional partial differential equations , 2011, J. Comput. Appl. Math..

[18]  Mingrong Cui.  Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation , 2012, Numerical Algorithms.

[19]  V. Uchaikin.  Fractional Derivatives for Physicists and Engineers , 2013 .

[20]  D. Shi,et al.  Superconvergence of a New Nonconforming Mixed Finite Element Scheme for Elliptic Problem , 2013 .

[21]  Yang Liu,et al.  A mixed finite element method for a time-fractional fourth-order partial differential equation , 2014, Appl. Math. Comput..

[22]  Zhi-Zhong Sun,et al.  Finite difference methods for the time fractional diffusion equation on non-uniform meshes , 2014, J. Comput. Phys..

[23]  Zhimin Zhang,et al.  Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations , 2015, 1511.03453.

[24]  Yang Liu,et al.  Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem , 2015, Comput. Math. Appl..

[25]  Bangti Jin,et al.  An analysis of the L1 Scheme for the subdiffusion equation with nonsmooth data , 2015, 1501.00253.

[26]  Fawang Liu,et al.  Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations , 2016, Appl. Math. Lett..

[27]  Shi Dong-yang,et al.  Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation , 2016 .

[28]  Xin Liao,et al.  A new nonconforming mixed finite element scheme for second order eigenvalue problem , 2016, Appl. Math. Comput..

[29]  Yu’e Ma,et al.  A superconvergent nonconforming mixed finite element method for the Navier–Stokes equations , 2016 .

[30]  Dongyang Shi,et al.  Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation , 2016, Appl. Math. Comput..

[31]  Fawang Liu,et al.  Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation , 2016 .

[32]  Bangti Jin,et al.  Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations , 2017, SIAM J. Sci. Comput..

[33]  Jose L. Gracia,et al.  Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation , 2017, SIAM J. Numer. Anal..

[34]  Pan Chen,et al.  Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations , 2017, J. Sci. Comput..

[35]  N. Ford,et al.  An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data , 2017 .

[36]  Zhi‐zhong Sun,et al.  Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme , 2017 .

[37]  Yubin Yan,et al.  An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data , 2018, SIAM J. Numer. Anal..