Explicit polynomial preserving trace liftings on a triangle

M. Ainsworth, L. Demkowicz

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7 Citations (Scopus)

Abstract

We give an explicit formula for a right inverse of the trace operator from the Sobolev space H1(T) on a triangle T to the trace space H1/2(T) on the boundary. The lifting preserves polynomials in the sense that if the boundary data are piecewise polynomial of degree N, then the lifting is a polynomial of total degree at most N and the lifting is shown to be uniformly stable independently of the polynomial order. Moreover, the same operator is shown to provide a uniformly stable lifting from L2(T) to H1/2(T). Finally, the lifting is used to construct a uniformly bounded right inverse for the normal trace operator from the space H(div; T) to H-1/2(T) which also preserves polynomials. Applications to the analysis of high order numerical methods for partial differential equations are indicated.
Original languageEnglish
Pages (from-to)640-658
Number of pages19
JournalMathematische Nachrichten
Volume282
Issue number5
DOIs
Publication statusPublished - May 2009

Keywords

  • trace lifting
  • polynomial extension
  • polynomial lifting
  • domain decomposition
  • p-version finite element method
  • spectral element method

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