报告题目：Petrov-Galerkin and indirect finite element methods for space-fractional diffusion equations with variable-coefficients
报告时间：6.21下午（周四）15:00-16:00
报告地点：18#918会议室
报告人：朱升峰
报告摘要：
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 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 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 post-processed by a fractional differentiation. It reduces numerically the computational work and the memory requirement. We prove that the corresponding high-order methods achieve high-order convergence rates even though the true solutions are not smooth. Numerical results are presented.
报告人简介：朱升峰博士，华东师范大学数学科学学院副教授。2006年本科毕业于浙江大学数学系，2011年获得浙江大学计算数学博士学位。2011年7月起到华东师范大学工作，2013-2014年在洛桑联邦理工学院做博士后，2014年12月晋升为副教授。目前主要研究领域涉及微分方程数值解、形状优化、等几何分析。
