HIERARCHIC MODELS OF HELMHOLTZ PROBLEMS ON THIN DOMAINS
Klaus Gerdes, Christoph Schwab · Mathematical Models and Methods in Applied Sciences · 1998
The Helmholtz equation in a three-dimensional plate is approximated by a hierarchy of two-dimensional models. Computable a posteriori error estimators of the modeling 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.