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 Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
 Speaker: Prof. Yanmin Zhao, School of Mathematics and Statistics, Xuchang University Inviter: 唐贻发 Title: Finite Element Approximations for Multi-Term Time Fractional Diusion Equations Time & Venue: 2017.5.21 9:00-10:00 N714 Abstract: Some diffusion processes of practical situations can be described more accurately by multi-term time fractional diffusion equations than single-term ones. We focuses on numerical approximations of nonconforming and conforming FEMs for the two-dimensional multi-term time fractional diffusion equation. Firstly, two unconditionally stable fully-discrete approximate schemes are established by using a modified L1 approximation and spatial FEM. Moreover, by employing the Crouzeix-Raviart type $EQ_1^{rot}$ nonconforming element, temporal optimal order error estimates and spatial optimal convergence rates in both $L^2$-norm and broken energy norm are proposed without restrictions between time step and mesh size. At the same time, the spatial global superconvergence and temporal convergence of order $O(h^2+\tau^{2-\alpha})$ for the original variable in $H^1$-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where $h$ and $\tau$ are the step sizes in space and time, respectively. Finally, several numerical results have been provided to give an insight into the efficiency and reliability of the theoretical analysis.

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