Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement
Year: 2024
Author: Hermenegildo Borges De Oliveira, Nuno David Lopes
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1013
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 3 : pp. 315–352
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: 2d Navier-Stokes feedback forces CD-FEM existence and uniqueness consistency and stability error analysis.
Author Details
Hermenegildo Borges De Oliveira Email
Nuno David Lopes Email