Discontinuous Galerkin method for fractional convection-diffusion equations
主 题: Discontinuous Galerkin method for fractional convection-diffusion equations
报告人: Qinwu Xu (School of Mathematical Science, PKU)
时 间: 2015-05-26 14:00 - 15:00
地 点: Room 29 at Quan Zhai, BICMR
In this talk, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. Based on the proposed method, a high order discretization is obtained for fractional Laplacian. Then, a discontinuous Galerkin method is proposed for fractional convection-diffusion equations with a superdiffusion operator of order α (1 < α < 2) defined through the fractional Laplacian. The fractional Laplacian of order α is expressed as a composite of first order derivatives and a fractional integral of order 2 ? α. The fractional convection-diffusion problem is expressed as a system of low order differential/integral equations, and a local discontinuous Galerkin method is proposed for the equations. We prove stability and optimal order of convergence O(h^(k+1)) for the fractional diffusion problem, and an order of convergence of O(h^(k+1/2)) is established for the general fractional convection-diffusion problem. The analysis is confirmed by numerical examples.