The weak element method applied to Helmholtz type equations
The author considers numerical methods for the solution of equations such as the two-dimensional Helmholtz equation for the intermediate frequency range. The domain is partitioned into small elements and the solution is approximated in each element by a set of exponentials with continuity conditions across the boundaries of the elements being specified. The approximations are determined through the optimization of variational expressions, and error estimates are obtained. Tables are given using the results of numerical calculations for a number of problems. The author suggests that the methods discussed will be useful when there is an adequate local approximation of oscillatory behaviour.
scientific article; zbMATH DE number 3988658