Volume 17, Issue 1
The Property of the Branch of Nonsingular Finite Element/Finite Volume Solutions to the Stationary Navier-Stokes Equations and Its Application

Jian Li & Yinnian He

Int. J. Numer. Anal. Mod., 17 (2020), pp. 42-53.

Published online: 2020-02

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  • Abstract

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.

  • Keywords

Stationary Navier-Stokes equations, finite element methods, finite volume methods, the branch of nonsingular solutions, inf-sup condition, large data.

  • AMS Subject Headings

65N30, 76D06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jiaaanli@gmail.com (Jian Li)

heyn@mail.xjtu.edu.cn (Yinnian He)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-42, author = {Li , Jian and He , Yinnian}, title = {The Property of the Branch of Nonsingular Finite Element/Finite Volume Solutions to the Stationary Navier-Stokes Equations and Its Application}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {1}, pages = {42--53}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13639.html} }
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.

Jian Li & Yinnian He. (2020). The Property of the Branch of Nonsingular Finite Element/Finite Volume Solutions to the Stationary Navier-Stokes Equations and Its Application. International Journal of Numerical Analysis and Modeling. 17 (1). 42-53. doi:
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