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A note on the Navier-Stokes IBVP with small data in $L^n$
Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem
1. | Departamento de Matemáticas, Universidad de Oviedo, Facultad de Ciencias, Calvo Sotelo s/n, 33007 Oviedo, Spain |
2. | Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile |
References:
[1] |
D. N. Arnold, F. Brezzi and J. Douglas, PEERS: A new mixed finite element method for plane elasticity, Japan J. Appl. Math., 1 (1984), 347-367.
doi: 10.1007/BF03167064. |
[2] |
D. N. Arnold, R. S. Falk and R. Winther, Mixed finite element methods for linear elasticity with weakly imposed symmetry, Math. Comp., 76 (2007), 1699-1723.
doi: 10.1090/S0025-5718-07-01998-9. |
[3] |
A. Bermúdez, R. Durán, M. A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes, SIAM J. Numer. Anal., 32 (1995), 1280-1295.
doi: 10.1137/0732059. |
[4] |
A. Bermúdez, R. Durán and R. Rodríguez, Finite element solution of incompressible fluid-structure vibration problems, Internat. J. Numer. Methods Engrg., 40 (1997), 1435-1448.
doi: 10.1002/(SICI)1097-0207(19970430)40:8<1435::AID-NME119>3.0.CO;2-P. |
[5] |
A. Bermúdez, P. Gamallo, L. Hervella-Nieto, R. Rodríguez and D. Santamarina, Fluid-structure Acoustic Interaction, Computational Acoustics of Noise Propagation in Fluids. Finite and Boundary Element Methods (eds. S. Marburg and B. Nolte), Springer, 2008. |
[6] |
A. Bermúdez and R. Rodríguez, Finite element analysis of sloshing and hydroelastic vibrations under gravity, RAIRO - Math. Model. Numer. Anal. ($M^2AN$), 33 (1999), 305-327.
doi: 10.1051/m2an:1999117. |
[7] |
D. Boffi, Finite element approximation of eigenvalue problems, Acta Numerica, 19 (2010), 1-120.
doi: 10.1017/S0962492910000012. |
[8] |
D. Boffi, F. Brezzi and M. Fortin, Reduced symmetry elements in linear elasticity, Comm. Pure Appl. Anal., 8 (2009), 95-121.
doi: 10.3934/cpaa.2009.8.95. |
[9] |
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3172-1. |
[10] |
M. Dauge, Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions, Lecture Notes in Mathematics, 1341, Springer, Berlin, 1988. |
[11] |
J. Descloux, N. Nassif and J. Rappaz, On spectral approximation. Part 1: The problem of convergence, RAIRO Anal. Numér., 12 (1978), 97-112. |
[12] |
G. N. Gatica, A. Márquez and S. Meddahi, Analysis of the coupling of Lagrange and Arnold-Falk-Winther finite elements for a fluid-solid interaction problem in 3D, SIAM J. Numer. Anal., 50 (2012), 1648-1674.
doi: 10.1137/110836705. |
[13] |
P. Grisvard, Problèmes aux limites dans les polygones. Mode d'emploi, EDF, Bulletin de la Direction des Études et Recherches (Serie C), 1 (1986), 21-59. |
[14] |
R. Hiptmair, Finite elements in computational electromagnetism, Acta Numerica, 11 (2002), 237-339.
doi: 10.1017/S0962492902000041. |
[15] |
L. Kiefling and G. C. Feng, Fluid-structure finite element vibration analysis, AIAA J., 14 (1976), 199-203.
doi: 10.2514/3.61357. |
[16] |
S. Meddahi, D. Mora and R. Rodríguez, Finite element spectral analysis for the mixed formulation of the elasticity equations, SIAM J. Numer. Anal., 51 (2013), 1041-1063.
doi: 10.1137/120863010. |
[17] |
S. Meddahi, D. Mora and R. Rodríguez, Finite element analysis for a pressure-stress formulation of a fluid-structure interaction spectral problem, Comput. Math. Appl., 68 (2014), 1733-1750.
doi: 10.1016/j.camwa.2014.10.016. |
[18] |
H. J.-P. Morand and R. Ohayon, Fluid Structure Interaction, J. Wiley & Sons, Chichester, 1995. |
show all references
References:
[1] |
D. N. Arnold, F. Brezzi and J. Douglas, PEERS: A new mixed finite element method for plane elasticity, Japan J. Appl. Math., 1 (1984), 347-367.
doi: 10.1007/BF03167064. |
[2] |
D. N. Arnold, R. S. Falk and R. Winther, Mixed finite element methods for linear elasticity with weakly imposed symmetry, Math. Comp., 76 (2007), 1699-1723.
doi: 10.1090/S0025-5718-07-01998-9. |
[3] |
A. Bermúdez, R. Durán, M. A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes, SIAM J. Numer. Anal., 32 (1995), 1280-1295.
doi: 10.1137/0732059. |
[4] |
A. Bermúdez, R. Durán and R. Rodríguez, Finite element solution of incompressible fluid-structure vibration problems, Internat. J. Numer. Methods Engrg., 40 (1997), 1435-1448.
doi: 10.1002/(SICI)1097-0207(19970430)40:8<1435::AID-NME119>3.0.CO;2-P. |
[5] |
A. Bermúdez, P. Gamallo, L. Hervella-Nieto, R. Rodríguez and D. Santamarina, Fluid-structure Acoustic Interaction, Computational Acoustics of Noise Propagation in Fluids. Finite and Boundary Element Methods (eds. S. Marburg and B. Nolte), Springer, 2008. |
[6] |
A. Bermúdez and R. Rodríguez, Finite element analysis of sloshing and hydroelastic vibrations under gravity, RAIRO - Math. Model. Numer. Anal. ($M^2AN$), 33 (1999), 305-327.
doi: 10.1051/m2an:1999117. |
[7] |
D. Boffi, Finite element approximation of eigenvalue problems, Acta Numerica, 19 (2010), 1-120.
doi: 10.1017/S0962492910000012. |
[8] |
D. Boffi, F. Brezzi and M. Fortin, Reduced symmetry elements in linear elasticity, Comm. Pure Appl. Anal., 8 (2009), 95-121.
doi: 10.3934/cpaa.2009.8.95. |
[9] |
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3172-1. |
[10] |
M. Dauge, Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions, Lecture Notes in Mathematics, 1341, Springer, Berlin, 1988. |
[11] |
J. Descloux, N. Nassif and J. Rappaz, On spectral approximation. Part 1: The problem of convergence, RAIRO Anal. Numér., 12 (1978), 97-112. |
[12] |
G. N. Gatica, A. Márquez and S. Meddahi, Analysis of the coupling of Lagrange and Arnold-Falk-Winther finite elements for a fluid-solid interaction problem in 3D, SIAM J. Numer. Anal., 50 (2012), 1648-1674.
doi: 10.1137/110836705. |
[13] |
P. Grisvard, Problèmes aux limites dans les polygones. Mode d'emploi, EDF, Bulletin de la Direction des Études et Recherches (Serie C), 1 (1986), 21-59. |
[14] |
R. Hiptmair, Finite elements in computational electromagnetism, Acta Numerica, 11 (2002), 237-339.
doi: 10.1017/S0962492902000041. |
[15] |
L. Kiefling and G. C. Feng, Fluid-structure finite element vibration analysis, AIAA J., 14 (1976), 199-203.
doi: 10.2514/3.61357. |
[16] |
S. Meddahi, D. Mora and R. Rodríguez, Finite element spectral analysis for the mixed formulation of the elasticity equations, SIAM J. Numer. Anal., 51 (2013), 1041-1063.
doi: 10.1137/120863010. |
[17] |
S. Meddahi, D. Mora and R. Rodríguez, Finite element analysis for a pressure-stress formulation of a fluid-structure interaction spectral problem, Comput. Math. Appl., 68 (2014), 1733-1750.
doi: 10.1016/j.camwa.2014.10.016. |
[18] |
H. J.-P. Morand and R. Ohayon, Fluid Structure Interaction, J. Wiley & Sons, Chichester, 1995. |
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