A Right-Inverse for the Divergence Operator in Spaces of Piecewise Polynomials. Application to the p-Version of the Finite Element Method.

Abstract

In the first part of this paper we study in detail the properties of the divergence operator acting on continuous piecewise polynomials; more specifically, we characterize the range and prove the existence of a maximal right-inverse whose norm grows at most algebraically with the degree of the piecewise polynomials. In the last part of this paper we apply these results to the p-version of the Finite Element Method for a nearly incompressible material with homogeneous Dirichlet boundary conditions. We show that the p-version maintains optimal convergence rates in the limit as the Poisson ratio approaches 1/2. This fact eliminates the need for any reduced integration such as customarily used in connection with the more standard h-version of the Finite Element Method. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1982
Accession Number
ADA116172

Entities

People

  • Michael Vogelius

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Computer Science
  • Contracts
  • Convergence
  • Equations
  • Finite Element Analysis
  • Materials
  • Mathematics
  • Military Research
  • New York
  • North Carolina
  • Numerical Analysis
  • Poisson Ratio
  • Polynomials
  • Theorems
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space