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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the stability analysis of boundary conditions for the wave equation by energy methods. I. The homogeneous case


Authors: T. Ha-Duong and P. Joly
Journal: Math. Comp. 62 (1994), 539-563
MSC: Primary 35L05; Secondary 35B35, 65N99
MathSciNet review: 1216259
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Abstract: We reconsider the stability theory of boundary conditions for the wave equation from the point of view of energy techniques. We study, for the case of the homogeneous half-space, a large class of boundary conditions including the so-called absorbing conditions. We show that the results of strong stability in the sense of Kreiss, studied from the point of view of the modal analysis by Trefethen and Halpern, always correspond to the decay in time of a particular energy. This result leads to the derivation of new estimates for the solution of the associated mixed problem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1216259-2
PII: S 0025-5718(1994)1216259-2
Keywords: Absorbing boundary conditions, well-posedness, energy estimates
Article copyright: © Copyright 1994 American Mathematical Society