Influence of boundary layers over the rate of convergence in a penalization method for a 1-D wave equation

摘要

For domain penalization methods, there can be a gap between the expected speed of convergence and the observed one, by numerical means. Such a gap has been observed by Paccou, et al. [A. Paccou, G. Chiavassa, J. Liandrat, K. Schneider, A penalization method applied to the wave equation, C. R. Mecanique 333 (2005) 79-85], concerning the penalization of a wave equation. We answer here one of their questions by proving that the observed lack in convergence speed is clearly related to the formation of boundary layers on one side of the boundary.