A new family of mixed finite elements for the linear elastodynamic problem

SIAM Journal on Numerical Analysis

Volumn 39, Issue 6, 2002, Pages 2109-2132

  Becache E ^a   Joly, P ^a   Tsogka, C ^a  

^a INRIA   (France)

Author keywords

Elastodynamics; Mass lumping; Mixed finite elements

Indexed keywords

EID: 0036556456     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999359189     Document Type: Article

References (28)

1. M. AMARA AND J. THOMAS, Equilibrium finite elements for the linear elastic problem, Numer. Math., 33 (1979), pp. 367-383.
2. D. N. ARNOLD, F. BREZZI, AND J. DOUGLAS, PEERS: A new mixed finite element for plane elasticity, Japan J. Appl. Math., 1 (1984), pp. 347-367.
3. B. A. AULD, Acoustic Fields and Elastic Waves in Solids, Vol. I, John Wiley, New York, 1973.
4. B. A. AULD, Acoustic Fields and Elastic Waves in Solids, Vol. II, John Wiley, New York, 1973.
5. I. BABUSKA, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), pp. 179-192.
6. G. A. BAKER AND V. A. DOUGALIS, The effect of quadrature errors on finite element approximations for second order hyperbolic equations, SIAM J. Numer. Anal., 13 (1976), pp. 577-598.
7. E. BÉCACHE, P. JOLY, AND C. TSOGKA, Eléments finis mixtes et condensation de masse en élastodynamique linéaire. I Construction, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), pp. 545-550.
8. E. BÉCACHE, P. JOLY, AND C. TSOGKA, Mixed Finite Elements, Strong Symmetry and Mass Lumping for Elastic Waves, Technical report 3717, INRIA, Rocquencourt, France, 1999.
9. E. BÉCACHE, P. JOLY, AND C. TSOGKA, An analysis of new mixed finite elements for the approximation of wave propagation problems, SIAM J. Numer. Anal., 37 (2000), pp. 1053-1084.
10. E. BÉCACHE, P. JOLY, AND C. TSOGKA, Fictitious domains, mixed finite elements and perfectly matched layers for 2d elastic wave propagation, J. Comput. Acoust., 9 (2001), pp. 1175-1202.
11. J. BÉRENGER, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), pp. 185-200.
12. J. BÉRENGER, Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 127 (1996), pp. 363-379.
13. F. BREZZI, On the existence uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Ser. Rouge, 8 (1974), pp. 129-151.
14. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
15. F. COLLINO AND C. TSOGKA, Application of the pml absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, 66 (2001), pp. 294-307.
16. P. DAVIS AND P. RABINOWITZ, Methods of Numerical Integration, Academic Press, Orlando, FL, 1985.
17. T. GEVECI, On the application of mixed finite element methods to the wave equations, Math. Model. Numer. Anal., 22 (1988), pp. 243-250.
18. V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag, Berlin, 1986.
19. C. JOHNSON AND B. MERCIER, Some equilibrium finite element methods for two-dimensional elasticity problems, Numer. Math., 30 (1978), pp. 103-116.
20. C. G. MAKRIDAKIS, On mixed finite element methods for linear elastodynamics, Numer. Math., 61 (1992), pp. 235-260.
21. M. E. MORLEY, A family of mixed finite elements for linear elasticity, Numer. Math., 55 (1989), pp. 633-666.
22. 3, Numer. Math., 50 (1986), pp. 57-81.
23. R. STENBERG, On the construction of optimal mixed finite element methods for the linear elasticity Problem, Numer. Math., 48 (1986), pp. 447-462.
24. R. STENBERG, A family of mixed finite elements for the elasticity problem, Numer. Math., 53 (1988), pp. 513-538.
25. R. STENBERG, A technique for analysing finite element methods for viscous incompressible flow, Internat. J. Numer. Methods Fluids, 11 (1990), pp. 935-948.
26. R. STENBERG, Error analysis of some finite element methods for the Stokes problem, Math. Comp., 54 (1990), pp. 495-508.
27. V. THOMÉE, Galerkin Finite Elements Methods for Parabolic Problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin, 1984.
28. N. TORDJMAN, Eléments finis d'ordre élevé avec condensation de masse pour l'équation des ondes, Ph.D. thesis, Université Paris IX, Paris, France, 1995.