TY - JOUR T1 - The Property of the Branch of Nonsingular Finite Element/Finite Volume Solutions to the Stationary Navier-Stokes Equations and Its Application AU - Li , Jian AU - He , Yinnian JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 42 EP - 53 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13639.html KW - Stationary Navier-Stokes equations, finite element methods, finite volume methods, the branch of nonsingular solutions, inf-sup condition, large data. AB -

In this paper, a branch of nonsingular solutions of the stationary Navier-Stokes equations are investigated, which are unique on a neighborhood, and mostly isolated without relying on very stringent requirement on the small data. We summarize and develop an equivalent definition of nonsingular solutions of finite element/finite volume methods in the same framework. Furthermore, we establish the equivalent definition of a branch of singular solutions of finite element methods for the coupled Navier-Stokes/Darcy equations.