Numerical Solution of Burger`s Type Equation Using Finite Element Collocation method with Strang Splitting

Authors : Yusuf UÇAR, Murat YAĞMURLU, İhsan ÇELİKKAYA

Pages : 29-45

Doi:10.36753/mathenot.598635

View : 33 | Download : 10

Publication Date : 2020-03-20

Article Type : Research Paper

Abstract :The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation U_{t}+UU_{x}=vU_{xx} two simpler sub problems U_{t}+UU_{x}=0 and  U_{t}-vU_{xx}=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 insert ignore into journalissuearticles values(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 ‖e‖₁, L₂ and L_{∞} in the literature and have made a comparison between exact and a numerical solution.
Keywords : Strang Splitting, Burgers Equation, Collocation method, Finite Element method, Cubic B Spline Basis

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