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.
Keywords: Homotopy method, continuous finite element method, Burgers’ equation
Hao, Wenrui 1 ; Yang, Yong 1
@article{M2AN_2019__53_5_1629_0,
author = {Hao, Wenrui and Yang, Yong},
title = {Convergence of a homotopy finite element method for computing steady states of {Burgers{\textquoteright}} equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1629--1644},
year = {2019},
publisher = {EDP Sciences},
volume = {53},
number = {5},
doi = {10.1051/m2an/2018046},
zbl = {1446.65092},
mrnumber = {3991489},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2018046/}
}
TY - JOUR AU - Hao, Wenrui AU - Yang, Yong TI - Convergence of a homotopy finite element method for computing steady states of Burgers’ equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 1629 EP - 1644 VL - 53 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2018046/ DO - 10.1051/m2an/2018046 LA - en ID - M2AN_2019__53_5_1629_0 ER -
%0 Journal Article %A Hao, Wenrui %A Yang, Yong %T Convergence of a homotopy finite element method for computing steady states of Burgers’ equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 1629-1644 %V 53 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2018046/ %R 10.1051/m2an/2018046 %G en %F M2AN_2019__53_5_1629_0
Hao, Wenrui; Yang, Yong. Convergence of a homotopy finite element method for computing steady states of Burgers’ equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 5, pp. 1629-1644. doi: 10.1051/m2an/2018046
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