Higher-Order Method for the Viscous Burgers Equation Based on Spatial Local Discontinuous Galerkin Approximation and Temporal Spectral Deferred Correction Evolution

In this paper, a higher-order method to solve the viscous Burgers equation is constructed and analysed. The main idea of the method is based on a proper selection of the numerical fluxes, a higher-order spatiotemporal evolution method which combines the local discontinuous Galerkin (LDG) method in the spatial direction and the spectral deferred correction (SDC) method in the temporal direction is proposed. Theoretically, the L² stability and the optimal error estimation for the spatial semi-discrete LDG method are proved, and the stability of the fully discrete method is given. Numerical examples are displayed to show the effectiveness of the proposed method.