CONVERGENCE OF A HOMOTOPY FINITE ELEMENT METHOD FOR COMPUTING STEADY STATES OF BURGERS' EQUATION

In this paper, the convergence of a homotopy method (1.1) for solving the steady state problem of Burgers' equation is considered. When nu is fixed, we prove that the solution of (1.1) converges to the unique steady state solution as epsilon -> 0, which is independent of the initial conditions. Numerical examples are presented to confirm this conclusion by using the continuous finite element method. In contrast, when nu = epsilon -> 0, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.