The weak element method applied to Helmholtz type equations
type: Item
instance of: scholarly article
title: The weak element method applied to Helmholtz type equations
zbMATH Open document ID: 0611.65070
DOI: 10.1016/0168-9274(86)90043-7
author: Charles I. Goldstein
published in: Applied Numerical Mathematics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 78A45
zbMATH DE Number: 3988658
zbMATH Keywords: scattering
zbMATH Keywords: diffraction
zbMATH Keywords: exponential basis functions
zbMATH Keywords: finite element
zbMATH Keywords: highly oscillatory solution
zbMATH Keywords: weak elements
zbMATH Keywords: two-dimensional Helmholtz equation
zbMATH Keywords: intermediate frequency range
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: 0168-9274(86)90043-7
OpenAlex ID: W1967101574
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description: scientific article; zbMATH DE number 3988658