Frequency-domain analysis of time-integration methods for semidiscrete finite element equations-part II: Hyperbolic and parabolic-hyperbolic problems

• Published in: International journal for numerical methods in engineering Vol. 51; no. 3; pp. 351 - 376
• Main Authors: Muğan, Ata, Hulbert, Gregory M.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.05.2001
• Subjects: finite element methods; frequency-domain analysis; hyperbolic and parabolic-hyperbolic problems; semidiscrete equations; time-integration methods
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.135

Time‐integration methods for semidiscrete finite element equations of hyperbolic and parabolic– hyperbolic types are analysed in the frequency domain. The discrete‐time transfer functions of six popular methods are derived, and subsequently the forced response characteristics of single modes are studied in the frequency domain. Three characteristic numbers are derived which eliminate the parameter dependence of the frequency responses. Frequency responses and L2‐norms of the phase and magnitude errors are calculated, and comparisons are given of the methods. As shown; the frequency‐domain analysis explains all time‐domain properties of the methods, and gives more insight into the subject. Copyright © 2001 John Wiley & Sons, Ltd.