王金凤1, 尹保利2, 刘洋2, 李宏2
王金凤, 尹保利, 刘洋, 李宏. 四阶分数阶扩散波动方程的两网格混合元快速算法[J]. 计算数学, 2022, 44(4): 496-507.
Wang Jinfeng, Yin Baoli, Liu Yang, Li Hong. A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION[J]. Mathematica Numerica Sinica, 2022, 44(4): 496-507.
Wang Jinfeng1, Yin Baoli2, Liu Yang2, Li Hong2
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[1] Wang J F, Yin B L, Liu Y, Li H, Fang Z C. A mixed element algorithm based on the modified L1 Crank-Nicolson scheme for a nonlinear fourth-order fractional diffusion-wave model[J]. Fractal Fract., 2021, 5:274. [2] Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam:North-Holland, 1978. [3] Nikan O, Tenreiro Machado J A, Golbabai A. Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments[J]. Appl. Math. Model., 2021, 89:819-836. [4] Agrawal O P. A general solution for a fourth-order fractional diffusion-wave equation defined in a bounded domain[J]. Comput. Struct., 2001, 79:1497-1501. [5] Jafari H, Dehghan M, Sayevand K. Solving a fourth-order fractional diffusion-wave equation in a bounded domain by decomposition method[J]. Numer. Meth. Part. Differ. Equ., 2008, 24:1115-1126. [6] Sun Z Z, Wu X N. A fully discrete difference scheme for a diffusion-wave system[J]. Appl. Numer. Math., 2006, 56(2):193-209. [7] Lin Y M, Xu C J. Finite difference/spectral approximations for the time-fractional diffusion equation[J]. J. Comput. Phys., 2007, 225:1533-1552. [8] Liu N, Liu Y, Li H, Wang J F. Time second-order finite difference/finite element algorithm for nonlinear time-fractional diffusion problem with fourth-order derivative term[J]. Comput. Math. Appl., 2018, 75:3521-3536. [9] Liu Y, Du Y W, Li H, He S, Gao W. Finite difference/finite element method for a nonlinear timefractional fourth-order reaction-diffusion problem[J]. Comput. Math. Appl., 2015, 70(4):573-591. [10] Liu Y, Fang Z C, Li H, He S. A mixed finite element method for a time-fractional fourth-order partial differential equation[J]. Appl. Math. Comput., 2014, 243:703-717. [11] Tariq H, Akram G. Quintic spline technique for time fractional fourth-order partial differential equation[J]. Numer. Meth. Part. Differ. Equ., 2017, 33(2):445-466. [12] Yang X H, Zhang H X, Xu D. Orthogonal spline collocation method for the fourth-order diffusion system[J]. Comput. Math. Appl., 2018, 75(9):3172-3185. [13] Du Y W, Liu Y, Li H, Fang Z C, He S. Local discontinuous Galerkin method for a nonlinear timefractional fourth-order partial differential equation[J]. J. Comput. Phys., 2017, 344:108-126. [14] Guo L, Wang Z B, Vong S K. Fully discrete local discontinuous Galerkin methods for some timefractional fourth-order problems, Int. J. Comput. Math., 2016, 93(10):1665-1682. [15] Ji C C, Sun Z Z, Hao Z P. Numerical algorithms with high spatial accuracy for the fourth-order fractional sub-diffusion equations with the first Dirichlet boundary conditions[J]. J. Sci. Comput., 2016, 66(3):1148-1174. [16] Hu X L, Zhang L M. On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems[J]. Appl. Math. Comput., 2012, 218(9):5019-5034. [17] Li X H, Wong Patricia J Y. An efficient numerical treatment of fourth-order fractional diffusionwave problems[J]. Numer. Meth. Part. Differ. Equ., 2018, 34(4):1324-1347. [18] Li D F, Zhang J W, Zhang Z M. Unconditionally optimal error estimates of a linearized galerkin method for nonlinear time fractional reaction-subdiffusion equations[J]. J. Sci. Comput., (2018) https://doi.org/10.1007/s10915-018-0642-9. [19] Grasselli M, Pierre M. A splitting method for the Cahn-Hilliard equation with inertial term[J]. Math. Model. Meth. Appl. Sci., 2010, 20(8):1363-1390. [20] Zeng F H, Li C P. A new Crank-Nicolson finite element method for the time-fractional subdiffusion equation[J]. Appl. Numer. Math., 2017, 121:82-95. [21] Xu J C. A novel two-grid method for semilinear elliptic equations[J]. SIAM J. Sci. Comput., 1994, 15:231-237. [22] Xu J C. Two-grid discretization techniques for linear and nonlinear PDEs[J]. SIAM J. Numer. Anal., 1996, 33:1759-1777. [23] Yan J L, Zhang Q, Zhu L, Zhang Z Y. Two-grid methods for finite volume element approximations of nonlinear Sobolev equations[J]. Numer. Funct. Anal. Optim., 2016, 37(3):391-414. [24] Chen Y P, Huang Y Q, Yu D H. A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations[J]. Int. J. Numer. Meth. Engrg., 2003, 57(2):193-209. [25] Chen Y P, Luan P, Lu Z. Analysis of two-grid methods for nonlinear parabolic equations by expanded mixed finite element methods[J]. Adv. Appl. Math. Mech., 2009, 1(6):830-844. [26] Dawson C N, Wheeler M F. Two-grid methods for mixed finite element approximations of nonlinear parabolic equations[J]. Contemp. Math., 1994, 180:191-203. [27] Wu L, Allen M B. A two grid method for mixed finite element solution of reaction-diffusion equations[J]. Numer. Meth. Part. Differ. Equ., 1999, 15:317-332. [28] Shi D Y, Yang H J. Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation[J]. Appl. Math. Comput., 2017, 310:40-47. [29] Chen C, Liu W. A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations[J]. J. Comput. Appl. Math., 2010, 233:2975-2984. [30] Li X, Rui H. A two-grid block-centered finite difference method for the nonlinear time-fractional parabolic equation[J]. J. Sci. Comput., 2017, 72(2):863-891. [31] Zhong L Q, Shu S, Wang J X, Xu J. Two-grid methods for time-harmonic Maxwell equations[J]. Numer. Linear Algebra Appl., 2013, 20(1):93-111. [32] Liu W, Rui H X, Hu F Z. A two-grid algorithm for expanded mixed finite element approximations of semi-linear elliptic equations[J]. Comput. Math. Appl., 2013, 66:392-402. [33] Liu Y, Du Y W, Li H, Li J C, He S. A two-grid mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with time-fractional derivative[J]. Comput. Math. Appl., 2015, 70(10):2474-2492. [34] Liu Y, Du Y W, Li H, Wang J F. A two-grid finite element approximation for a nonlinear timefractional Cable equation[J]. Nonlinear Dyn. 2016, 85:2535-2548. [35] Bu W P, Liu X T, Tang Y F, Yang J Y. Finite element multigrid method for multi-term time fractional advection diffusion equations[J]. Int. J. Model. Simulat.Sci. Comput. 2015, 6(1):1540001. |
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