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Title: 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 ν 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 ν = epsilon → 0, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.  more » « less
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ESAIM: Mathematical Modelling and Numerical Analysis
Medium: X
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National Science Foundation
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