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Volume 21, Issue 3
Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement

Hermenegildo Borges De Oliveira & Nuno David Lopes

DOI: 10.4208/ijnam2024-1013

Int. J. Numer. Anal. Mod., 21 (2024), pp. 315-352.

Published online: 2024-05

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  • Abstract

In this work, a stationary 2d Navier-Stokes problem with nonlinear feedback forces field is considered in the stream-function formulation. We use the Continuous/Discontinuous Finite Element Method (CD-FEM), with interior penalty terms, to numerically solve the associated boundary-value problem. For the associated continuous and discrete problems, we prove the existence of weak solutions and establish the conditions for their uniqueness. Consistency, stability and convergence of the method are also shown analytically. To validate the numerical model regarding its applicability and robustness, several test cases are carried out.

  • Keywords

2d Navier-Stokes, feedback forces, CD-FEM, existence and uniqueness, consistency and stability, error analysis.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-315, author = {Oliveira , Hermenegildo Borges De and Lopes , Nuno David}, title = {Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {3}, pages = {315--352}, abstract = {

In this work, a stationary 2d Navier-Stokes problem with nonlinear feedback forces field is considered in the stream-function formulation. We use the Continuous/Discontinuous Finite Element Method (CD-FEM), with interior penalty terms, to numerically solve the associated boundary-value problem. For the associated continuous and discrete problems, we prove the existence of weak solutions and establish the conditions for their uniqueness. Consistency, stability and convergence of the method are also shown analytically. To validate the numerical model regarding its applicability and robustness, several test cases are carried out.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1013}, url = {http://global-sci.org/intro/article_detail/ijnam/23127.html} }
TY - JOUR T1 - Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement AU - Oliveira , Hermenegildo Borges De AU - Lopes , Nuno David JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 315 EP - 352 PY - 2024 DA - 2024/05 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1013 UR - https://global-sci.org/intro/article_detail/ijnam/23127.html KW - 2d Navier-Stokes, feedback forces, CD-FEM, existence and uniqueness, consistency and stability, error analysis. AB -

In this work, a stationary 2d Navier-Stokes problem with nonlinear feedback forces field is considered in the stream-function formulation. We use the Continuous/Discontinuous Finite Element Method (CD-FEM), with interior penalty terms, to numerically solve the associated boundary-value problem. For the associated continuous and discrete problems, we prove the existence of weak solutions and establish the conditions for their uniqueness. Consistency, stability and convergence of the method are also shown analytically. To validate the numerical model regarding its applicability and robustness, several test cases are carried out.

Oliveira , Hermenegildo Borges De and Lopes , Nuno David. (2024). Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement. International Journal of Numerical Analysis and Modeling. 21 (3). 315-352. doi:10.4208/ijnam2024-1013
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