Details

Autor(en) / Beteiligte

• XU, QINWU
• HESTHAVEN, JAN S.

Titel

DISCONTINUOUS GALERKIN METHOD FOR FRACTIONAL CONVECTION-DIFFUSION EQUATIONS

Ist Teil von

• SIAM journal on numerical analysis, 2014-01, Vol.52 (1), p.405-423

Ort / Verlag

Philadelphia: Society for Industrial and Applied Mathematics

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We propose a discontinuous Galerkin method for fractional convection-diffusion equations with a superdiffusion operator of order α(1 < α < 2) defined through the fractional Laplacian. The fractional operator 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 scheme is proposed for the equations. We prove stability and optimal order of convergence O(hk+1) for the fractional diffusion problem, and an order of convergence of O(hk+1⁄2) is established for the general fractional convection-diffusion problem. The analysis is confirmed by numerical examples.