Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation
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Fawang Liu | Ian Turner | I. Turner | Fawang Liu | Yanmin Zhao | Y. M. Zhao | Y. D. Zhang | D. Y. Shi | Yadong Zhang | D. Shi
[1] Zhi-Zhong Sun,et al. Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation , 2014, J. Sci. Comput..
[2] Fawang Liu,et al. Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation , 2015, Appl. Math. Comput..
[3] Igor M. Sokolov,et al. Fractional diffusion in inhomogeneous media , 2005 .
[4] Yaolin Jiang,et al. Analytical solutions for the multi-term time–space fractional advection–diffusion equations with mixed boundary conditions , 2013 .
[5] K. Burrage,et al. Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain , 2012 .
[6] I. L. El-Kalla,et al. Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations , 2010 .
[7] Juan J. Nieto,et al. Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain , 2015 .
[8] Hermann Brunner,et al. Numerical simulations of 2D fractional subdiffusion problems , 2010, J. Comput. Phys..
[9] Hehu Xie,et al. Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations , 2013, Applications of Mathematics.
[10] S. Das,et al. Analytical solution of a fractional diffusion equation by variational iteration method , 2009, Comput. Math. Appl..
[11] Fawang Liu,et al. Numerical solution of the space fractional Fokker-Planck equation , 2004 .
[12] Luming Zhang,et al. An analysis of a second order difference scheme for the fractional subdiffusion system , 2016 .
[13] Yufeng Xu,et al. Numerical and analytical solutions of new generalized fractional diffusion equation , 2013, Comput. Math. Appl..
[14] Fenling Wang,et al. EQ1rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations , 2013 .
[15] Changpin Li,et al. A novel compact ADI scheme for the time-fractional subdiffusion equation in two space dimensions , 2016, Int. J. Comput. Math..
[16] Fawang Liu,et al. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain , 2012, Comput. Math. Appl..
[17] Q. Lin,et al. Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation , 2005 .
[18] Shipeng Mao,et al. High accuracy analysis of two nonconforming plate elements , 2009, Numerische Mathematik.
[19] Chao-Jiang Xu,et al. EQ1rot nonconforming finite element approximation to Signorini problem , 2013 .
[20] Bangti Jin,et al. The Galerkin finite element method for a multi-term time-fractional diffusion equation , 2014, J. Comput. Phys..
[21] Ying Zhao,et al. Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations , 2014, J. Sci. Comput..
[22] Carsten Carstensen,et al. P1-Nonconforming Finite Elements on Triangulations into Triangles and Quadrilaterals , 2012, SIAM J. Numer. Anal..
[23] Jincheng Ren,et al. Efficient numerical approximation of the multi-term time fractional diffusion-wave equations , 2015 .
[24] Fawang Liu,et al. New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation , 2008, SIAM J. Numer. Anal..
[25] Jingjun Zhao,et al. Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations , 2013 .
[26] Approximate solutions to fractional subdiffusion equations , 2011, 1103.1586.
[27] D. Benson,et al. Application of a fractional advection‐dispersion equation , 2000 .
[28] Jincheng Ren,et al. Efficient and stable numerical methods for multi-term time fractional sub-diffusion equations , 2014 .
[29] Dongwoo Sheen,et al. A new cubic nonconforming finite element on rectangles , 2015 .
[30] Pan Chen,et al. Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations , 2017, J. Sci. Comput..
[31] Fawang Liu,et al. Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy , 2015, SIAM J. Sci. Comput..
[32] Fawang Liu,et al. The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation , 2013, SIAM J. Sci. Comput..
[33] Shipeng Mao,et al. CONVERGENCE AND SUPERCONVERGENCE OF A NONCONFORMING FINITE ELEMENT ON ANISOTROPIC MESHES , 2007 .
[34] Bangti Jin,et al. An analysis of the L1 Scheme for the subdiffusion equation with nonsmooth data , 2015, 1501.00253.
[35] Xuan Zhao,et al. Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions , 2013, J. Comput. Phys..
[36] Ali H. Bhrawy,et al. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations , 2015, J. Comput. Phys..
[37] R. Gorenflo,et al. Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.
[38] Jun Hu,et al. Constructing both lower and upper bounds for the eigenvalues of elliptic operators by nonconforming finite element methods , 2014, Numerische Mathematik.
[39] Jiye Yang,et al. Finite element multigrid method for multi-term time fractional advection diffusion equations , 2015, Int. J. Model. Simul. Sci. Comput..
[40] M. Meerschaert,et al. Numerical methods for solving the multi-term time-fractional wave-diffusion equation , 2012, Fractional calculus & applied analysis.
[41] Xiaoyuan Yang,et al. A nonconforming rectangular finite element pair for the Darcy–Stokes–Brinkman model , 2013 .
[42] K. Diethelm. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .
[43] Chao Xu,et al. Anisotropic Nonconforming $${ EQ}_1^{rot}$$ Quadrilateral Finite Element Approximation to Second Order Elliptic Problems , 2013, J. Sci. Comput..
[44] Fawang Liu,et al. The analytical solution and numerical solution of the fractional diffusion-wave equation with damping , 2012, Appl. Math. Comput..
[45] Mohammed Al-Refai,et al. Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives , 2015, Appl. Math. Comput..
[46] Zhiyuan Li,et al. Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients , 2013, Appl. Math. Comput..
[47] Zhi-Zhong Sun,et al. A compact finite difference scheme for the fractional sub-diffusion equations , 2011, J. Comput. Phys..
[48] Jingtang Ma,et al. High-order finite element methods for time-fractional partial differential equations , 2011, J. Comput. Appl. Math..
[49] R. Gorenflo,et al. AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES , 1999 .
[50] Shao-chunChen,et al. AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS , 2005 .
[51] R. Rannacher,et al. Simple nonconforming quadrilateral Stokes element , 1992 .
[52] Dongwoo Sheen,et al. P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems , 2003, SIAM J. Numer. Anal..