| Issue |
ESAIM: M2AN
Volume 53, Number 5, September-October 2019
|
|
|---|---|---|
| Page(s) | 1629 - 1644 | |
| DOI | https://doi.org/10.1051/m2an/2018046 | |
| Published online | 12 August 2019 | |
Article
Convergence of a homotopy finite element method for computing steady states of Burgers’ equation
Department of Mathematics, The Pennsylvania State University, 16802-6400 University Park, PA, USA
* Corresponding author: yyy5104@psu.edu
Received:
7
July
2017
Accepted:
17
July
2018
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 ε → 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 = ε →, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.
Mathematics Subject Classification: 58B05 / 65M12 / 65M60
Key words: Homotopy method / continuous finite element method / Burgers’ equation
© EDP Sciences, SMAI 2019
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