Mixed Isogeometric Analysis of the Brinkman Equation

This study focuses on numerical solution to the Brinkman equation with mixed Dirichlet–Neumann boundary conditions utilizing isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) within the Galerkin method framework. The authors suggest using different choices of compatible NUR...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-06, Vol.11 (12), p.2750
Main Authors: Ouadefli, Lahcen El, Moutea, Omar El, Akkad, Abdeslam El, Elkhalfi, Ahmed, Vlase, Sorin, Scutaru, Maria Luminița
Format: Article
Language:English
Subjects:
Analysis
Approximation
Boundary conditions
Brinkman
CAD-CAM systems
Computer programs
Computer-aided design
convergence
Dirichlet problem
finite element
Finite element analysis
Galerkin method
isogeometric analysis
Knots
Mathematical analysis
Mathematics
NURBS
Nédélec
Partial differential equations
Velocity
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Summary:This study focuses on numerical solution to the Brinkman equation with mixed Dirichlet–Neumann boundary conditions utilizing isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) within the Galerkin method framework. The authors suggest using different choices of compatible NURBS spaces, which may be considered a generalization of traditional finite element spaces for velocity and pressure approximation. In order to investigate the numerical properties of the suggested elements, two numerical experiments based on a square and a quarter of an annulus are discussed. The preliminary results for the Stokes problem are presented in References.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11122750