The Partition of Unity Finite Element Method

Abstract

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity finite element method is that finite element spaces of any desired regularity can be constructed very easily. Moreover the method is of "meshless" type. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a-posteriori error estimation for this new method are also proved. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1995
Accession Number
ADA301760

Entities

People

  • Ivo Babuška
  • J. M. Melenk

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Coefficients
  • Construction
  • Coverings
  • Differential Equations
  • Elastic Properties
  • Equations
  • Finite Element Analysis
  • Helmholtz Equations
  • Interpolation
  • Partial Differential Equations
  • Physical Sciences
  • Plane Waves
  • Three Dimensional
  • Two Dimensional
  • Waves

Fields of Study

  • Engineering
  • Mathematics

Readers

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

Technology Areas

  • Space