Numerical solution of Burgers' equation by quadratic B-spline finite elements

In this paper, a Galerkin quadratic B-spline finite element method is used to solve numerically the one-dimensional Burgers' equation reduced by the Hopf-Cole transformation. The performance of the method is tested on two model problems involving moderately Reynolds numbers with known exact solutions. The obtained numerical results show that the method is efficient, robust and reliable for solving Burgers' equation accurately even involving high Reynolds numbers for which the exact solution fails. Computed results are compared with other numerical results in the literature. A stability analysis of the method is also investigated.