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Report 1996-12
Hierarchic models of Helmholtz problems on thin domains
K. Gerdes and C.Schwab
Abstract: The Helmholtz equation in a three-dimensional plate is approximated by a hierarchy of two-dimensional models. Computable a posteriori error estimators of the modelling error in exponentially weighted norms are derived, and sharp, computable estimates for their effectivity indices are also obtained. The necessity of including, besides polynomials, a certain number of trigonometric director functions into the Ansatz, in order to prevent pollution effects at high wave numbers is demonstrated both theoretically and computationally.
Paper: Available as PDF (187 KB) or as hardcopy to order reports@sam.math.ethz.ch.
Publishing information: Mathematical Models & Methods, in: Applied Sciences, Vol. 8, (1998), p. 1-35
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