Finite Element Solution to the Helmholtz Equation with High Wave Number. Part 1. The h-Version of the FEM

Abstract

The h-version of the finite element method with piecewise linear approximation has been applied to solve a one-dimensional model problem for the Helmholtz equation. The main practical purpose of the investigation is to lay theoretical ground for safe rules of the thumb how to choose the mesh width of the FE-model depending on the wavenumber. In this context we present new results for stability and error estimation of the FE-solution. Following the analysis, numerical results are discussed. In a second paper we will study the h-p-method for Helmholtz problems.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1993
Accession Number
ADA277396

Entities

People

  • Frank Ihlenburg
  • Ivo Babuška

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundary Element Methods
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Helmholtz Equations
  • Inequalities
  • Integral Equations
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Physical Sciences
  • Theorems
  • Universities
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)