Numerical study of two-dimensional Burgers' equation by using a continuous Galerkin method *

In this article, we use space-time continuous Galerkin (STCG) method to find the numerical solution for twodimensional (2D) Burgers' equation. The STCG method differs from conventional finite element methods, both the spatial and temporal variables are discretized by finite element method, thus it can easily obtain the high order accuracy in both time and space directions and the corresponding discrete scheme is unconditionally stable. We demonstrate the existence and uniqueness of numerical solution by using Brouwer's fixed point theorem and give the a priori error estimates without needing to satisfy the limitation of the space-time mesh ratio condition. At last, we provide two numerical examples to confirm the efficiency of the method. Moreover, the numerical experiments reveal that the proposed method can handle the bigger Reynolds number than the existing literatures in the case of the absence of stabilization techniques and has the better stability as well as does not need to impose a limitation on the time step size.