Improving the rate of convergence of high-order finite elements on polyhedra I: A priori estimates

Constantin Bacuta, Victor Nistor, Ludmil Zikatanov

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Let k be a sequence of triangulations of a polyhedron n and let S k be the associated finite element space of continuous, piecewise polynomials of degree m . Let u k S k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S k ensures optimal rates of convergence for the sequence u k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet-Neumann boundary conditions on a polygon.

Original languageEnglish (US)
Pages (from-to)613-639
Number of pages27
JournalNumerical Functional Analysis and Optimization
Volume26
Issue number6
DOIs
StatePublished - Sep 1 2005

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High-order Finite Elements
A Priori Estimates
Polyhedron
Rate of Convergence
Boundary conditions
Sobolev spaces
Dirichlet Boundary Conditions
Triangulation
Weak Approximation
Poisson Problem
Optimal Rate of Convergence
Weighted Sobolev Spaces
Piecewise Polynomials
Polynomials
Approximation Property
Elliptic Systems
Finite Element Approximation
Neumann Boundary Conditions
Polygon
Finite Element

All Science Journal Classification (ASJC) codes

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this

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Improving the rate of convergence of high-order finite elements on polyhedra I : A priori estimates. / Bacuta, Constantin; Nistor, Victor; Zikatanov, Ludmil.

In: Numerical Functional Analysis and Optimization, Vol. 26, No. 6, 01.09.2005, p. 613-639.

Research output: Contribution to journalArticle

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