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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Mathematical analysis of absorbing boundary conditions for the wave equation: the corner problem
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by Olivier Vacus PDF
Math. Comp. 74 (2005), 177-200 Request permission


Our goal in this work is to establish the existence and the uniqueness of a smooth solution to what we call in this paper the corner problem, that is to say, the wave equation together with absorbing conditions at two orthogonal boundaries. First we set the existence of a very smooth solution to this initial boundary value problem. Then we show the decay in time of energies of high order—higher than the order of the boundary conditions. This result shows that the corner problem is strongly well-posed in spaces smaller than in the half-plane case. Finally, specific corner conditions are derived to select the smooth solution among less regular solutions. These conditions are required to derive complete numerical schemes.
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Additional Information
  • Olivier Vacus
  • Affiliation: CEA/CESTA, 33 114 Le Barp Cedex, France
  • Email:
  • Received by editor(s): May 26, 2002
  • Received by editor(s) in revised form: June 29, 2003
  • Published electronically: July 22, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 177-200
  • MSC (2000): Primary 78A40, 65N12; Secondary 65M12, 46N40
  • DOI:
  • MathSciNet review: 2085407