High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative
Authors:
- 6 March 2019
- journal article
- research article
- Published by Wiley in Numerical Methods for Partial Differential Equations
- Vol. 35 (4) , 1588-1612
Abstract
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 Pk, k = 0, 1, 2, 3, elements are provided to verify our theoretical results.Keywords
Funding Information
- National Natural Science Foundation of China (11661058, 11761053)
- Natural Science Foundation of Inner Mongolia Autonomous Region (2016MS0102, 2017MS0107)
This publication has 49 references indexed in Scilit:
- Chebyshev Wavelets Method for Solution of Nonlinear Fractional Integrodifferential Equations in a Large IntervalAdvances in Mathematical Physics, 2013
- Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic EquationsSIAM Journal on Numerical Analysis, 2013
- Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equationIMA Journal of Numerical Analysis, 2011
- A compact finite difference scheme for the fractional sub-diffusion equationsJournal of Computational Physics, 2011
- A local discontinuous Galerkin method for directly solving Hamilton–Jacobi equationsJournal of Computational Physics, 2011
- A note on the finite element method for the space-fractional advection diffusion equationComputers & Mathematics with Applications, 2010
- Local discontinuous Galerkin methods for the generalized Zakharov systemJournal of Computational Physics, 2010
- Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equationApplied Mathematics and Computation, 2009
- Fractal mobile/immobile solute transportWater Resources Research, 2003
- Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian GridsSIAM Journal on Numerical Analysis, 2001