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Velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity.
- Source :
- Calcolo; Dec2021, Vol. 58 Issue 4, p1-25, 25p
- Publication Year :
- 2021
-
Abstract
- We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The weak formulation includes least-squares terms arising from the constitutive equation and from the incompressibility condition, and we show that it satisfies the hypotheses of the Babuška-Brezzi theory. Repeating the arguments of the continuous analysis, the stability and solvability of the discrete problem are established. The method is suited for any Stokes inf-sup stable finite element pair for velocity and pressure, while for vorticity any generic discrete space (of arbitrary order) can be used. A priori and a posteriori error estimates are derived using two specific families of discrete subspaces. Finally, we provide a set of numerical tests illustrating the behaviour of the scheme, verifying the theoretical convergence rates, and showing the performance of the adaptive algorithm guided by residual a posteriori error estimation. [ABSTRACT FROM AUTHOR]
- Subjects :
- VISCOSITY
FINITE element method
ALGORITHMS
A posteriori error analysis
VORTEX motion
Subjects
Details
- Language :
- English
- ISSN :
- 00080624
- Volume :
- 58
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Calcolo
- Publication Type :
- Academic Journal
- Accession number :
- 153242890
- Full Text :
- https://doi.org/10.1007/s10092-021-00433-6