Space‐time finite elements incorporating characteristics for the burgers' equation

Abstract A new finite element method is presented for the numerical solution of the Burgers' equation. The method is based on a weighted residual formulation in which the method of characteristics is incorporated by employing isoparametric space–time elements with the sides joining the nodes at subsequent time levels oriented along the characteristic lines of the hyperbolic partial differential equation associated with the Burgers' equation. This method is capable of solving the Burgers' equation accurately for values of viscosity ranging from very small to large. The utility and accuracy of the method are demonstrated by a number of examples and a comparison of the numerical results with the exact solution is presented in one case.