%A Yanhua Shi,Yadong Zhang,Fenling Wang,Yanmin Zhao,Pingli Wang %T High Accuracy Analysis of Linear Triangular Element for Time Fractional Diffusion Equations %0 Journal Article %D 2019 %J Acta mathematica scientia,Series A %R %P 839-850 %V 39 %N 4 %U {http://121.43.60.238/sxwlxbA/CN/abstract/article_15910.shtml} %8 2019-08-26 %X

In this paper, based on linear triangular element and improved $L1$ approximation, a fully-discrete scheme is proposed for time fractional diffusion equations with $\alpha$ order Caputo fractional derivative. Firstly, the unconditional stability is proved. Secondly, by employing the properties of the element and Ritz projection operator, superclose analysis for the projection operator is deduced with order $O(h^2+\tau^{2-\alpha})$. Further more, combining with relationship between the interpolation operator and Ritz projection, superclose analysis for the interpolation operator is also investigated with order $O(h^2+\tau^{2-\alpha})$. And then, the superconvergence result is obtained through the interpolated postprocessing technique. Finally, numerical results are provided to show the validity of our theoretical analysis.