Abstract:
Abstract:The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been split according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation Ut + UUx = vUxx into two simpler sub problems Ut + UUx = 0 and Ut − vUxx = 0 have been obtained. A discretization process has been performed for each of these sub-problems and the stability analyzes have been carried out by Fourier (von Neumann) series method. Then, both sub-problems have been solved using the Strang splitting technique to obtain numerical results. To see the effectiveness of the present method, which is a combination of finite element method and Strang splitting technique, we have calculated the frequently used error norms kek1 , L2 and L∞ in the literature and have made a comparison between exact and a numerical solution.
