Fast calculation based on a spatial two-grid finite element algorithm for a nonlinear space–time fractional diffusion model |
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Authors: | Yang Liu Nan Liu Hong Li Jinfeng Wang |
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Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, China;2. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, China |
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Abstract: | In this article, a spatial two-grid finite element (TGFE) algorithm is used to solve a two-dimensional nonlinear space–time fractional diffusion model and improve the computational efficiency. First, the second-order backward difference scheme is used to formulate the time approximation, where the time-fractional derivative is approximated by the weighted and shifted Grünwald difference operator. In order to reduce the computation time of the standard FE method, a TGFE algorithm is developed. The specific algorithm is to iteratively solve a nonlinear system on the coarse grid and then to solve a linear system on the fine grid. We prove the scheme stability of the TGFE algorithm and derive a priori error estimate with the convergence result O(Δt2 + hr + 1 − η + H2r + 2 − 2η) . Finally, through a two-dimensional numerical calculation, we improve the computational efficiency and reduce the computation time by the TGFE algorithm. |
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Keywords: | error analysis nonlinear space–time fractional diffusion model two-grid finite element algorithm |
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