Numerical solutions to the 1-D burgers’ equation by a cubic hermite finite element method
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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 L2 and L1 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.