
A TWOGRID FINITE ELEMENT APPROXIMATION FOR NONLINEAR TIME FRACTIONAL TWOTERM MIXED SUBDIFFUSION AND DIFFUSION WAVE EQUATIONS
Yanping Chen, Qiling Gu, Qingfeng Li, Yunqing Huang
Journal of Computational Mathematics
2022, 40 (6):
936954.
DOI: 10.4208/jcm.2104m20200332
In this paper, we develop a twogrid method (TGM) based on the FEM for 2D nonlinear time fractional twoterm mixed subdiffusion and diffusion wave equations. A twogrid algorithm is proposed for solving the nonlinear system, which consists of two steps: a nonlinear FE system is solved on a coarse grid, then the linearized FE system is solved on the fine grid by Newton iteration based on the coarse solution. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space derivatives and the finite difference scheme for the time Caputo derivative with order
α ∈ (1, 2) and
α
_{1} ∈ (0, 1). Numerical stability and optimal error estimate
O(
h
^{r+1} +
H
^{2r+2} +
τ
^{min3α,2α1}}) in
L
^{2}norm are presented for twogrid scheme, where t, H and h are the time step size, coarse grid mesh size and fine grid mesh size, respectively. Finally, numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm.
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