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Hierarchic models of Helmholtz problems on thin domains

by K. Gerdes and Ch. Schwab

(Report number 1996-12)

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.

Keywords:

@Techreport{GS96_195,
  author = {K. Gerdes and Ch. Schwab},
  title = {Hierarchic models of Helmholtz problems on thin domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-12.pdf },
  year = {1996}
}

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