A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations

Abstract

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^2−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.