Dispersion and pollution of the FEM solution for the helmholtz equation in one, two and three dimensions

International Journal for Numerical Methods in Engineering

Volumn 46, Issue 4, 1999, Pages 471-499

  Deraemaeker, Arnaud ^a   Babuška, Ivo ^b   Bouillard, Philippe ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Acoustics; Dispersion; Helmholtz equation; Pollution

Indexed keywords

GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; TOPOLOGY;

HELMHOLTZ EQUATION; POLLUTION EFFECT; TOPOLOGY TRIANGLES;

FINITE ELEMENT METHOD;

ACOUSTICS; DISPERSION; FLOW; POLLUTION;

EID: 0344549300     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6     Document Type: Article

References (19)

1. Babuška I, Ihlenburg F, Paik ET, Sauter SA. A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Computational Methods in Applied Mechanical Engineering 1995; 128:325-359.
2. Babuška I, Sauter S. Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wavenumber? SIAM Journal of Numerical Analysis 1997; 34:2392-2423.
3. Franca L, Farhat C, Macedo A, Lesoinne M. Residual-free bubbles for the Helmholtz equation, International Journal for Numerical Methods in Engineering 1997; 40:4003-4009.
4. Franca L, Macedo A. A two-level finite element method and its application to the Helmholtz equation. International Journal for Numerical Methods in Engineering 1998; 43:23-32.
5. 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; 38:371-397.
6. Ihlenburg F, Babuška I. Finite element solution to the Helmholtz equation with high wavenumber part I: the h-version of the FEM. Computational Methods in Applied Mechanical Engineering 1995; 30:9-37.
7. Ihlenburg F, Babuška I. Finite element solution to the Helmholtz equation with high wavenumber part II: the h-p-version of the FEM. SIAM Journal of Numerical Analysis 1997; 34:315-358.
8. Ihlenburg 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; 38:4207-4235.
9. Babuška I, Ihlenburg F, Strouboulis T, Gangaraj SK. A posteriori error estimation for finite element solutions of Helmholtz equation. Part I. International Journal for Numerical Methods in Engineering 1997; 40:3443-3462. Part II, International Journal for Numerical Methods in Engineering 1997; 40:3883-3890.
10. Babuška I, Ihlenburg F, Strouboulis T, Gangaraj SK. A posteriori error estimation for finite element solutions of Helmholtz equation. Part I. International Journal for Numerical Methods in Engineering 1997; 40:3443-3462. Part II, International Journal for Numerical Methods in Engineering 1997; 40:3883-3890.
11. Bouillard P, Ihlenburg F. Error estimation and adaptivity for the finite element solution in acoustics. Advances in Adaption Computational Methods in Mechanics 1998; ISBN 008-043327-8:477-492.
12. Bouillard P. Influence of the pollution on the admissible field error estimation for FE solutions of the Helmholtz equation. International Journal for Numerical Methods in Engineering 1998, to be published.
13. Harari I, Hughes TJR. Finite element methods for the Helmholtz equation in an exterior domain: model problems. Computational Methods in Applied Mechanical Engineering 1991; 87:59-96.
14. Bouillard P, Suleau S. Element-free Galerkin method for Helmholtz problems: formulation and numerical assessment of the pollution effect. Computational Method in Mechanical Engineering 1998; 162:317-335.
15. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
16. Babuška I. The Fourier transform in the theory of difference equation and its applications. Archiwum Mechaniki Stosowanes 1959; 11:349-381.
17. Babuška I, Strouboulis T, Upadhyay CS, Gangaraj SK, Copps K. Validation of a posteriori error estimators by a numerical approach. International Journal for Numerical Methods in Engineering 1994; 37:1073-1123.
18. Demkowicz L, Walsh T, Gerdes K, Bajer A. 2D hp-adaptive finite element package fortran 90 implementation (2Dhp90), Ticam Report 98-14, 1998.
19. Franca L, Russo A. Unlocking with Residual-free bubbles. Computational Methods in Applied Mechanical Engineering 1997; 142:361-364.