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

Year 2020, Volume: 8 Issue: 1, 29 - 45, 20.03.2020

Yusuf Uçar , Murat Yağmurlu , İhsan Çelikkaya

https://doi.org/10.36753/mathenot.598635

Cited By: 5

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 (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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