Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
type: Item
instance of: scholarly article
title: Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
zbMATH Open document ID: 0838.65108
DOI: 10.1016/0898-1221(95)00144-N
author: F. Ihlenburg
author: Ivo Babuška
publication date: 1996-06-03T00:00:00Z
review text: This paper examines the quality of the discrete numerical solutions to the Helmholtz equation \(\Delta u + k^2u = f\) where \(k\) is the wave number. These equations arise in problems of wave scattering and fluid-solid-interaction. It is shown that the relative error in the finite element solution in \(H^1\) seminorm is \[ e_1 \leq C_1kh + C_2 k^3 h^2 \] where \(h\) is the step length of the meshes. The first term on the right hand side of the inequality is the approximation error and the second term is due to numerical pollution.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 820322
zbMATH Keywords: error bound
zbMATH Keywords: high wave number
zbMATH Keywords: \(h\)-version
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: wave scattering
zbMATH Keywords: fluid-solid-interaction
zbMATH Keywords: finite element
reviewed by: Brian L. Burrows
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 820322