High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative | Zendy

Zhang Min | Zendy; Liu Yang | Zendy; Li Hong | Zendy

Premium

High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative

Author(s) -

Zhang Min,

Liu Yang,

Li Hong

Publication year - 2019

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22366

Subject(s) - mathematics , fractal , fractional calculus , rate of convergence , convergence (economics) , stability (learning theory) , a priori and a posteriori , discontinuous galerkin method , galerkin method , derivative (finance) , mathematical analysis , order (exchange) , finite element method , physics , computer science , computer network , channel (broadcasting) , philosophy , epistemology , finance , machine learning , financial economics , economics , thermodynamics , economic growth

In this article, a local discontinuous Galerkin (LDG) method is studied for numerically solving the fractal mobile/immobile transport equation with a new time Caputo–Fabrizio fractional derivative. The stability of the LDG scheme is proven, and a priori error estimates with the second‐order temporal convergence rate and the ( k + 1) th order spatial convergence rate are derived in detail. Finally, numerical experiments based on P k , k = 0, 1, 2, 3, elements are provided to verify our theoretical results.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research