Numerical solutions to the 1-D Burgers' equation by a cubic Hermite finite element method

Abstract

In this paper, a finite element method (FEM) with cubic Hermite element is presented to acquire the numerical solution (ns) for the one-dimensional Burgers' equation (BE). We show that our scheme is unconditionally stable by using the Von-Neumann technique. To test the accuracy and efficiency of the method, the acquired numerical results are compared with the exact solutions (es). Furthermore, we compute L-2 and L-infinity error norms to test the accuracy of our results with those available in the literature. Finally, some graphical representations for the numerical results are provided.