This talk is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of the state and co-state are decomposed into singular and regular parts, and some growth estimates are obtained for the singular parts. Following the variational discretization concept, a full discretization is applied to the state and co-state equations by using conforming linear finite element method in space and piecewise constant discontinuous Galerkin method in time. Error estimates are derived by employing the growth estimates. In particular, graded temporal grids are adopted to obtain the first-order temporal accuracy. Finally, numerical experiments are provided to verify the theoretical results.  

XIE, Xiaoping received his B.S. degree in mathematics and M.S. degree in computational mathematics from Sichuan University, China in 1993 and 1996 respectively, and his Ph.D degree from Aeronautical Computing Technique Research Institute, China in 2000. He got a teaching position at Sichuan University in 1996, and became an associate professor of mathematics in 2001 and then a full professor in 2004.  He received a Humboldt Research Fellowship from the Alexander von Humboldt Foundation in 2008. His research interests include numerical analysis for partial differential equations, finite element methods and their applications.
Member of editorial board：  
《数值计算与计算机应用》、《Mathematical Problems in Engineering》、《Numerical Analysis and Applicable Mathematics》、《Fractal and Fractional》(Topic Editor)