内容简介：

Fractional advection-diffusion equation (FADE) is a promising model to describe anomalous diffusion phenomenon which has been observed in turbulent flow, solute transport in porous media, just name a few. In this talk, an in-depth numerical analysis of such FADE utilizing the finite element method (FEM) is presented. A traditional Galerkin finite element formulation of a FADE may yield numerical oscillations in the solution depending on not only the advection term but also the diffusion term with fractional derivative order We show that this stability issue can be characterized by a fractional element Peclet number, which generalizes the definition of traditional element Peclet number. To address this oscillatory behavior, a Petrov-Galerkin method is formulated using a fractional stabilization parameter with a compact formula to eliminate the oscillatory behavior. Steady state and transient 1D/2D cases of the pure fractional diffusion and FADEs are implemented to demonstrate the effectiveness and accuracy of the proposed formulation.

报告人简介：

Dr. Yanping Lian is a Postdoctoral Fellow in Professor Wing Kam Liu's group at the Northwestern University. His research area includes meshfree methods to material and structural subjected to extreme loading conditions involving in explosion, impact/penetration, and additive manufacturing, and a recent focus on stable and high-accuracy numerical methods to fractional partial differential equations. Dr. Lian has papers published on journals including Computer Methods in Applied Mechanics and Engineering, International Journal of Impact Engineering, Computational Mechanics, and so on. He serves as the reviewer of Computational Mechanics, International Journal of Mechanics and Materials in Design. He received his Ph.D. degree in mechanics from Tsinghua University in 2012, and won the award of Outstanding Doctoral Dissertation of Tsinghua University.