TY - JOUR
T1 - A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations
AU - Yuan , Wenping
AU - Chen , Yanping
AU - Huang , Yunqing
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 818
EP - 837
PY - 2020
DA - 2020/08
SN - 10
DO - http://doi.org/10.4208/eajam.300919.240520
UR - https://global-sci.org/intro/article_detail/eajam/17963.html
KW - Time-fractional Burgers equation, Caputo fractional derivative, local discontinuous
Galerkin method, stability, convergence.
AB - <p style="text-align: justify;">A local discontinuous Galerkin finite element method for a class of time-fractional Burgers equations is developed. In order to achieve a high order accuracy, the
time-fractional Burgers equation is transformed into a first order system. The method
is based on a finite difference scheme in time and local discontinuous Galerkin methods
in space. The scheme is proved to be unconditionally stable and in linear case it has
convergence rate $\mathcal{O}$(τ<sup>2−α</sup>&nbsp;+ $h$<sup>$k$</sup><sup>+1</sup>), where $k$ ≥ 0 denotes the order of the basis functions
used. Numerical examples demonstrate the efficiency and accuracy of the scheme.</p>