HIGH ACCURACY ANALYSIS OF ANISOTROPIC LINEAR TRIANGULAR ELEMENT FOR MULTI-TERM TIME FRACTIONAL DIFFUSION EQUATIONS
Wang Fenling1, Fan Mingzhi1, Zhan Yanmin1, Shi Zhengguang2, Shi Dongyang3
1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China;
2. School of Economic Matnematics, Southwestern University of Finance and Economic, Chengdu 611130, China;
3. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 475001, China
High accuracy analysis of linear triangular element is proposed for two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivative on anisotropic meshes. Firstly, based on linear triangular element and modified L1 scheme, a fully-discrete approximate scheme is established and the unconditional stability analysis is investigated. Secondly, by use of the relationship between the interpolation operator and Riesz projection operator, superclose property is derived by related known high accuracy results. Moreover, the superconvergence estimate is obtained through the interpolation postprocessing technique. It is worth mentioning that the above superclose and superconvergence results will not be derived by the interpolation operator and Riesz projection operator alone. Finally, numerical results are provided to confirm the validity of our theoretical analysis. Furthermore, some popular finite elements of numerical approximation for the focused equation are investigated.
. HIGH ACCURACY ANALYSIS OF ANISOTROPIC LINEAR TRIANGULAR ELEMENT FOR MULTI-TERM TIME FRACTIONAL DIFFUSION EQUATIONS[J]. Mathematica Numerica Sinica, 2018, 40(3): 299-312.
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