The application of finite element method in burgers’ equation

Abstract

The main objective of this project is to provide the explanation of the application of Finite Element method in 1- dimensional Burgers’ equation. Burgers’ equation captures very important phenomena surrounding world. Its can be categorized as a parabolic, elliptic and hyperbolic partial differential equation. For this reason, Burgers equation is often used as a case study for testing and comparing computational technique. The 1- dimension Burgers’ equation is investigated and their results are compared with analytical solution of the problem. To solve the problem in finite element method, few concept are introduced such that calculus of variation, weight function, and weak formulation. A brief explaination of the calculation using Finite Element Method (FEM) is given. In this research, the Finite Element method algorithm is written in Matlab and Maple programme. Based on the numerical results, we can see from the behaviour of the graph , the solution is approching some limit as we increased the number of Reynolds. The error between numerical and analytical result becomes larger. We cay say that , FEM is a unique and useful technique and it is being extended to solve many problem in engineering and science area.