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

37 Scopus citations

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

All Science Journal Classification (ASJC) codes

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

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