Dispersion analysis of a non-conforming finite element method for the Helmholtz and elastodynamic equations

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 9, 2003, Pages 1381-1395

  Zyserman, Fabio I ^a   Gauzellino, Patricia M ^a   Santos, Juan E ^a,b  

^a UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Dispersion matrix; Non conforming finite elements; Phase and group velocities

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; VELOCITY;

ELASTODYNAMICS EQUATIONS;

NUMERICAL METHODS;

FINITE ELEMENT METHOD;

EID: 0242497935     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.822     Document Type: Article

References (18)

1. Douglas Jr J, Sheen D, Santos J. Approximation of scalar waves in the space-frequency domain. Mathematical Models and Methods in Applied Sciences 1994; 4(4):509-531.
2. Douglas Jr J, Santos J, Sheen D, Ye X. Non-conforming Galerkin methods based on quadrilateral elements for second order elliptic problems. Mathematical Modelling and Numerical Analysis 1999; 33:744.
3. Douglas Jr J, Santos J, Sheen D. Non-conforming Galerkin methods for the Helmholtz equation. Numerical Methods for Partial Differential Equations 2001; 17:475-494.
4. Gauzelino P, Santos J, Sheen D. Frequency domain wave propagation modeling in exploration seismology. Journal of Computational Acoustics 2001; 9(3):941-955.
5. Bayliss A, Goldstein C, Turkel E. On accuracy conditions for the numerical computation of waves. Journal of Computational Physics 1985; 59:396-404.
6. Thompson LL, Pinsky PM. A Galerkin least squares finite element method for the two dimensional Helmholtz equation. International Journal for Numerical Methods in Engineering 1995; 38(3):371-397.
7. Ihlemburg F, Babuška I. Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. International Journal for Numerical Methods in Engineering 1995; 38:3745-3774.
8. Ihlemburg F, Babuška I. Finite element solution of the Helmholtz equation with high wave number Part I: the h-version of the FEM. Computers and Mathematics with Applications 1995; 30(9):9-37.
9. Ihlemburg F, Babuška I. Finite element solution of the Helmholtz equation with high wave number Part II: the h-p-version of the FEM. SIAM Journal on Numerical Analysis 1997; 34(1):325-358.
10. Babuška I, Sauter S. Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM Journal on Numerical Analysis 1997; 34(6):2392-2423.
11. Bamberger A, Chavent G, Lailly P. Etude de schémas numériques pour les équations de I élastodynamique linéaire, Technical Report 41, INRIA, 1980.
12. Suiker A, Metrikine A, de Borst R. Comparison of the wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models. International Journal of Solids and Structures 2001; 38:1563-1583.
13. Biot MA. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics 1962; 33:1482-1498.
14. Ravazzoli CL, Douglas Jr J, Santos JE, Sheen D. On the solution of the equations of motion for nearly elastic solids in the frequency domain. In Anales de la IV Reunión de Trabajo en Procesamiento de la Información y Control, RPIC'91, 1991.
15. Sheen D, Douglas Jr J, Santos JE. Frequency-domain parallel algorithms for the approximation of acoustic and elastic waves. In Numerical Analysis (Finite Element Methods), 1993; 243-288.
16. Babuška I, Ihlemburg F, Paik E, Sauter S. A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Computer Methods in Applied Mechanics and Engineering 1995; 128:325-359.
17. Oberai A, Pinsky P. A residual-based finite element method for the Helmholtz equation. International Journal for Numerical Methods in Engineering 2000; 49:399-419.
18. Ihlemburg F, Babuška I, Sauter S. Reliability of finite element methods for the numerical computation of waves. Advances in Engineering Software 1997; 28(7):417-424.