### Abstract

Language | English |
---|---|

Pages | 640-658 |

Number of pages | 19 |

Journal | Mathematische Nachrichten |

Volume | 282 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2009 |

### Fingerprint

### Keywords

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

### Cite this

*Mathematische Nachrichten*,

*282*(5), 640-658. https://doi.org/10.1002/mana.200610762

}

*Mathematische Nachrichten*, vol. 282, no. 5, pp. 640-658. https://doi.org/10.1002/mana.200610762

**Explicit polynomial preserving trace liftings on a triangle.** / Ainsworth, M.; Demkowicz, L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Explicit polynomial preserving trace liftings on a triangle

AU - Ainsworth, M.

AU - Demkowicz, L.

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

KW - trace lifting

KW - polynomial extension

KW - polynomial lifting

KW - domain decomposition

KW - p-version finite element method

KW - spectral element method

U2 - 10.1002/mana.200610762

DO - 10.1002/mana.200610762

M3 - Article

VL - 282

SP - 640

EP - 658

JO - Mathematische Nachrichten

T2 - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 5

ER -