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Second-order absorbing boundary conditions for the wave equation in a rectangular domain

Author: Dongwoo Sheen
Journal: Math. Comp. 61 (1993), 595-606
MSC: Primary 65M60
MathSciNet review: 1192975
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Abstract: We study finite element methods for the wave equation in a rectangular domain with a second-order absorbing boundary condition imposed on the boundary. For this problem there seems to be no known finite element method, although many finite difference methods have been proposed. A third-order energy, however, will be introduced which will be utilized to reduce our original second-order problem to a first-order symmetric dissipative hyperbolic system. Then, for this first-order system a weak formulation will be given and continuous-time and discrete-time Galerkin procedures will be investigated. Error estimates will also be given.

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Keywords: Finite element method, absorbing boundary conditions, higher-order energy
Article copyright: © Copyright 1993 American Mathematical Society

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