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Finite element approximations of space-fractional diffusion equations with a variable-coefficient
Date: 2017/11/8             Browse: 27

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 

Abstract:

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.

Bio:

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