Dimensional reduction for Helmholtz's equation on a bounded domain |
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| Authors: | Kang-Man Liu Ivo Babuška |
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| Affiliation: | (1) Department of Mathematics, National Changhwa University of Education, Paisa Village, Changhwa 50058, Taiwan, R.O.C.; e-mail: kmliu@math.ncue.edu.tw , TW;(2) Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA , US |
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| Abstract: | Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990 |
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| Keywords: | Mathematics Subject Classification (1991): 65N12 65N15 65N30 |
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