A Galerkin finite element approach to Burgers' equation

摘要

A Galerkin finite element method is presented for the numerical solution of Burgers' equation. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a Crank–Nicolson approach involving a product approximation. It is shown that this method is capable of solving Burgers' equation accurately for a wide range of viscosity values. The results show that the new method performs better than the most of the methods available in the literature.