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Finite element approximations of space-fractional diffusion equations with a variable-coefficient
Date: 2017/11/8             Browse: 255

Speaker:     Associate Prof, Shengfeng Zhu, ECNU

Time:          Nov 8,  10:00 am.– 11:00 am.

Location:    Room 1A-200, SIST Building

Inviter:       Prof. Qifeng Liao 


Fractional diffusion equations have found increasingly more applications in recent years but introduce new mathematical and numerical difficulties. Galerkin formulation, which was proved to be coercive and well-posed for fractional diffusion equations with a constant diffusivity coefficient, may lose its coercivity for variable-coefficient problems. The corresponding finite element method fails to converge. We utilize the discontinuous Petrov-Galerkin framework to develop a Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations. We prove the well-posedness and optimal-order convergence. Moreover, we present an indirect finite element method, which reduces the solution of fractional diffusion equations to that of second-order diffusion equations postprocessed by a fractional differentiation. It reduces the computational work for the numerical solution of variable-coefficient fractional diffusion equations from O(N^3) to O(N) and the memory requirement from O(N^2) to O(N) on any quasi-uniform space partition.We prove that the corresponding high-order methods achieve high-order convergence rates even though the true solutions are not smooth, provided that the coefficient and source term of the problem have desired regularities. Numerical experiments are presented.


Since 2014, Associate Professor, Department of Mathematics, East China Normal University

2011--2014, Lecturer, Department of Mathematics, East China Normal University

2013--2014, Postdoc, CMCS, MATHICSE,  (EPFL) , Switzerland

2006--2011, Ph.D. in Computational Mathematics, Zhejiang University

2002--2006, B.S. in Computational Mathematics, Zhejiang University 

Research Interests:

Numerical Methods to Differential Equations

Shape Optimization

SIST-Seminar 17056