# Explicit polynomial preserving trace liftings on a triangle

Ainsworth, M. and Demkowicz, L.
(2009)
*Explicit polynomial preserving trace liftings on a triangle.*
Mathematische Nachrichten, 282 (5).
pp. 640-658.
ISSN 0025-584X

## 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.

Item type: | Article |
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ID code: | 19122 |

Keywords: | trace lifting, polynomial extension, polynomial lifting, domain decomposition, p-version finite element method, spectral element method, Mathematics, Mathematics(all) |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 19 May 2010 13:35 |

Last modified: | 27 Apr 2016 15:09 |

URI: | http://strathprints.strath.ac.uk/id/eprint/19122 |