convergence of a homotopy finite element method for computing steady states of Burgers' equation
convergence of a homotopy finite element method for computing steady states of Burgers' equation
复制标题
用于计算 Burgers 方程稳态的同伦有限元方法的收敛性
DOI：
10.1051/m2an/2018046
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Hao, Wenrui
中科院分区：
文献类型：
--
作者：
Yang, Yong;Hao, Wenrui
本文讨论了求解Burgers型方程稳态问题的同伦方法(1.1)的收敛问题。当ν固定时，我们证明了(1.1)的解收敛到唯一的定态解，即ε→0，它与初始条件无关。用连续有限元方法给出的数值算例验证了这一结论。相反，当ν=ε→时，我们从数值上证明了(1.1)所得到的定态解确实依赖于初始条件。
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.