Abstract
This paper is devoted to the numerical analysis of a family of finite element approximations for the axisymmetric, meridian Brinkman equations written in terms of the stream-function and vorticity. A mixed formulation is introduced involving appropriate weighted Sobolev spaces, where well-posedness is derived by means of the Babuška–Brezzi theory. We introduce a suitable Galerkin discretization based on continuous piecewise polynomials of degree k≥ 1 for all the unknowns, where its solvability is established using the same framework as the continuous problem. Optimal a priori error estimates are derived, which are robust with respect to the fluid viscosity, and valid also in the pure Darcy limit. A few numerical examples are presented to illustrate the convergence and performance of the proposed schemes.
Original language | English |
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Pages (from-to) | 348-364 |
Number of pages | 17 |
Journal | Journal of Scientific Computing |
Volume | 71 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Apr 2017 |
Externally published | Yes |
Keywords
- Axisymmetric domains
- Brinkman equations
- Error estimates
- Finite element method
- Stability analysis
- Stream-function and vorticity formulation