ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65N12, 65N15, 65N30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain $\Omega^d:=\Omega\times (-d,d)\subset {\Bbb R}^{n+1}$ by replacing them with systems of equations in $n-$ dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution $u$ and the dimensionally reduced solution $u_N$ of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between $u$ and $u_N$ in $H^1(\Omega^d)$ is estimated as $d$ and $N$ are fixed. Finally, some numerical experiments in a domain $\Omega=(0,1)\times (0,1)$ are given in order to compare theretical results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050298
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