Velocity‑vorticity‑pressure formulation for the Oseen problem with variable viscosity
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| Auteurs: | , , , , |
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| Format: | artículo original |
| Date de publication: | 2021 |
| Description: | 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 |
| Pays: | Kérwá |
| Institution: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Langue: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/86465 |
| Accès en ligne: | https://link.springer.com/article/10.1007/s10092-021-00433-6 https://hdl.handle.net/10669/86465 |
| Mots-clés: | Oseen equations Velocity-vorticity-pressure formulation Mixed finite element methods Variable viscosity A priori and a posteriori error analysis Adaptive mesh refinement |