A right-inverse for the divergence operator in spaces of piecewise polynomials - Application to the p-version of the finite element method

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Abstract

In the first part of this paper we study in detail the properties of the divergence operator acting on continuous piecewise polynomials on some fixed triangulation; 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.

Original languageEnglish (US)
Pages (from-to)19-37
Number of pages19
JournalNumerische Mathematik
Volume41
Issue number1
DOIs
StatePublished - Feb 1 1983
Externally publishedYes

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P-version
Piecewise Polynomials
Mathematical operators
Divergence
Finite Element Method
Polynomials
Reduced Integration
Finite element method
Optimal Convergence Rate
Poisson's Ratio
Poisson ratio
Triangulation
Operator
Dirichlet Boundary Conditions
Eliminate
Boundary conditions
Norm
Range of data
Standards

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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