The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
A stabilized finite element method for generalized stationary incompressible flows
Open accessAbstract
Abstract In this paper, we describe a finite element formulation for the numerical solution of the stationary incompressible Navier–Stokes equations including Coriolis forces and the permeability of the medium. The stabilized method is based on the algebraic version of the sub-grid scale approach. We first describe this technique for general systems of convection–diffusion–reaction equations and then we apply it to the linearized flow equations. The important point is the design of the matrix of stabilization parameters that the method has. This design is based on the identification of the stability problems of the Galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix. This, together with the convergence analysis of the linearized problem, leads to a simple expression for the stabilization parameters in the general situation considered in the paper. The numerical analysis of the linearized problem also shows that the method has optimal convergence properties.
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Cites
Mixed and Hybrid Finite Element Methods
(1991) · Springer Series in Computational Mathematics · doi:10.1007/978-1-4612-3172-1 · Cited by 6,390
The Mathematical Theory of Finite Element Methods
Brenner, S. C., & Scott, L. R. (2002) · Texts in Applied Mathematics · doi:10.1007/978-1-4757-3658-8 · Cited by 4,090
The Mathematical Theory of Finite Element Methods
Brenner, S. C., & Scott, L. R. (1994) · Texts in Applied Mathematics · doi:10.1007/978-1-4757-4338-8 · Cited by 2,188
Hughes, T. J. R. (1995) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(95)00844-9 · Cited by 1,807
Hughes, T. J. R., Franca, L. P., & Hulbert, G. M. (1989) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(89)90111-4 · Cited by 1,458
Hughes, T. J. R., Franca, L. P., & Balestra, M. (1986) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(86)90025-3 · Cited by 1,450
Stabilized finite element methods: II. The incompressible Navier-Stokes equations
Franca, L. P., & Frey, S. L. (1992) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(92)90041-h · Cited by 758
Stabilized finite element methods: I. Application to the advective-diffusive model
Franca, L. P., Frey, S. L., & Hughes, T. J. R. (1992) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(92)90143-8 · Cited by 650
Hughes, T. J. R., & Mallet, M. (1986) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(86)90152-0 · Cited by 573
Comparison of some finite element methods for solving the diffusion-convection-reaction equation
Codina, R. (1998) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/s0045-7825(97)00206-5 · Cited by 537
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Metadata
- Authors
- Codina, R.
- Venue
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Published
- 2001-02
- Volume
- 190
- Issue
- 20-21
- Pages
- 2681-2706
- ISSN
- 0045-7825 (ISSN-L)
- OpenAlex
- W1983570119
- Cited by
- 271
- References
- 17
- FWCI
- 12.96
- Type
- journal article
- Language
- en
- Open access
- green
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