Adaptive finite element techniques for the acoustic wave equation

Journal of Computational Acoustics

Volumn 9, Issue 2, 2001, Pages 575-591

  Bangerth, Wolfgang ^a   Rannacher, Rolf ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035596217     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X01000668     Document Type: Article

References (15)

1. W. Bangerth, "Adaptive Finite-Elemente-Methoden zur Lösung der Wellengleichung mit Anwendung in der Physik der Sonne," Diplomarbeit, Institut für Angewandte Mathematik, Universität Heidelberg, 1998.
2. R. Becker and R. Rannacher, "A feed-back approach to error control in finite element methods: Basic analysis and examples," East-West J. Num. Math. 4, 237 (1996).
3. W. Bangerth and R. Rannacher, "Finite element approximation of the acoustic wave equation: Error control and mesh adaptation," East-West J. Numer. Math. 7, 263 (1999).
4. D. A. French and T. E. Peterson, "A continuous space-time finite element method for the wave equation," Math. Comp. 65, 491 (1996).
5. R. Becker and R. Rannacher, "Weighted a posteriori error control in FE methods," Proceedings of ENUMATH 95, in Proceedings of ENUMATH 97, eds. H. G. Bock et al. (World Scientific, 1998).
6. K. Eriksson and C. Johnson, "An adaptive finite element method for linear elliptic problems," Math. Comp. 50, 361 (1988).
7. A. G. Butkovski, Green's Functions and Transfer Functions Handbook (Ellis Horwood Ltd., 1982).
8. D. W. Kelly, J. R. Gago, O. C. Zienkiewicz, and I. Babuška, "A posteriori error analysis and adaptive processes in the finite element method: Part I - Error analysis," Internat. J. Numer. Methods Engrg. 19, 1593 (1983).
9. W. Bangerth and G. Kanschat, "Concepts for object-oriented finite element software - the deal. II library," preprint 99-43, IWR Heidelberg, Oct. 1999. See also http://gaia.iwr.uni-heidelberg.de/deal/.
10. G. Kanschat, "Parallel and adaptive Galerkin methods for radiative transfer problems," Dissertation, Universität Heidelberg, 1996.
11. R. Becker and R. Rannacher, "A general concept of adaptivity in finite element methods with applications to problems in fluid and structural mechanics," in Grid Generation and Adaptive Algorithms, eds. M. Bern, J. E. Flaherty, and M. Luskin, Vol. 113 of IMA Volumes in Mathematics and its Applications (Springer, 1998).
12. X. D. Li and N.-E. Wiberg, "Implementation and adaptivity of a space-time finite element method for structural dynamics," Comput. Methods Appl. Mech. Engrg. 156, 211 (1998).
13. Z. P. Bažant, "Spurious reflection of elastic waves in nonuniform finite element grids," Comput. Methods Appl. Mech. Engrg. 16, 91 (1978).
14. I. Freid, "Accuracy of string element mass matrix," Comput. Methods Appl. Mech. Engrg. 20, 317 (1979).
15. I. Harari, "Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics," Comput. Methods Appl. Mech. Engrg. 140, 39 (1997).