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Approximation properties of lowest-order hexahedral Raviart–Thomas finite elements. (English. Abridged French version) Zbl 1071.65148

Summary: Basic interpolation results are settled for lowest-order hexahedral Raviart-Thomas finite elements. Convergence in H(div) is proved for regular families of asymptotically parallelepiped meshes. The need of the asymptotically parallelepiped assumption is demonstrated with a numerical example.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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[1] Arnold, D. N.; Boffi, D.; Falk, R. S., Approximation by quadrilateral finite elements, Math. Comp., 71, 909-922 (2002) · Zbl 0993.65125
[2] Arnold, D. N.; Boffi, D.; Falk, R. S., Quadrilateral \(H(div)\) finite elements, SIAM J. Numer. Anal., 42, 2429-2451 (2005) · Zbl 1086.65105
[3] Arnold, D. N.; Boffi, D.; Falk, R. S.; Gastaldi, L., Finite element approximation on quadrilateral meshes, Comm. Numer. Methods Engrg., 17, 805-812 (2001) · Zbl 0999.76073
[4] Babuška, I.; Osborn, J., Eigenvalue problems, (Ciarlet, P. G.; Lions, P. L., Handbook of Numerical Analysis, vol. II (1991), North-Holland: North-Holland Amsterdam), 641-787 · Zbl 0875.65087
[5] Bermúdez, A.; Durán, R.; Muschietti, M. A.; Rodríguez, R.; Solomin, J., Finite element vibration analysis of fluid-solid systems without spurious modes, SIAM J. Numer. Anal., 32, 1280-1295 (1995) · Zbl 0833.73050
[6] A. Bermúdez, P. Gamallo, M.R. Nogueiras, R. Rodríguez, Approximation of a structural acoustic vibration problem by hexahedral finite elements, submitted for publication; A. Bermúdez, P. Gamallo, M.R. Nogueiras, R. Rodríguez, Approximation of a structural acoustic vibration problem by hexahedral finite elements, submitted for publication
[7] Bermúdez, A.; Gamallo, P.; Rodríguez, R., A hexahedral face element for elastoacoustic vibration problems, J. Acoust. Soc. Amer., 109, 422-425 (2001)
[8] Bermúdez, A.; Gamallo, P.; Rodríguez, R., An hexahedral face element method for the displacement formulation of structural acoustics problems, J. Comput. Acoust., 9, 911-918 (2001)
[9] Bermúdez, A.; Hervella-Nieto, L.; Rodríguez, R., Finite element computation of three dimensional elastoacoustic vibrations, J. Sound Vib., 219, 277-304 (1999) · Zbl 1235.74267
[10] Bermúdez, A.; Rodríguez, R., Finite element computation of the vibration modes of a fluid-solid system, Comput. Methods Appl. Mech. Engrg., 119, 355-370 (1994) · Zbl 0851.73053
[11] Brezzi, F.; Fortin, M., Mixed and Hybrid Finite Element Methods (1991), Springer: Springer New York · Zbl 0788.73002
[12] Girault, V.; Raviart, P. A., Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms (1986), Springer-Verlag: Springer-Verlag Berlin · Zbl 0585.65077
[13] Nédélec, J. C., Mixed finite elements in \(R^3\), Numer. Math., 35, 315-341 (1980) · Zbl 0419.65069
[14] Raviart, P. A.; Thomas, J. M., A mixed finite element method for second order elliptic problems, (Galligani, I.; Magenes, E., Mathematical Aspects of Finite Element Methods. Mathematical Aspects of Finite Element Methods, Lecture Notes in Math., vol. 606 (1977), Springer-Verlag: Springer-Verlag Berlin), 292-315
[15] J.M. Thomas, Sur l’Analyse Numérique des Méthodes d’Éléments Finis Hybrides et Mixtes, Thèse de Doctorat d’Etat, Université Pierre et Marie Curie, Paris, 1977; J.M. Thomas, Sur l’Analyse Numérique des Méthodes d’Éléments Finis Hybrides et Mixtes, Thèse de Doctorat d’Etat, Université Pierre et Marie Curie, Paris, 1977
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