Stability analysis of model problems for elastodynamic boundary element discretizations

• Published in: Numerical methods for partial differential equations Vol. 12; no. 5; pp. 585 - 613
• Main Authors: Peirce, A., Siebrits, E.
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01-09-1996
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/(SICI)1098-2426(199609)12:5<585::AID-NUM4>3.0.CO;2-G

In the literature there is growing evidence of instabilities in standard time‐stepping schemes to solve boundary integral elastodynamic models [1]–[3]. In this article we use three distinct model problems to investigate the stability properties of various discretizations that are commonly used to solve elastodynamic boundary integral equations. Using the model problems, the stability properties of a large variety of discretization schemes are assessed. The features of the discretization procedures that are likely to cause instabilities can be established by means of the analysis. This new insight makes it possible to design new time‐stepping schemes that are shown to be more stable. © 1996 John Wiley & Sons, Inc.