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 -

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 $\mathcal{O}$(τ2−α + $h$$k$+1), where $k$ ≥ 0 denotes the order of the basis functions used. Numerical examples demonstrate the efficiency and accuracy of the scheme.