Explicit polynomial preserving trace liftings on a triangle

✍ Scribed by Mark Ainsworth; Leszek Demkowicz

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 252 KB
• Volume: 282
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610762

✦ Synopsis

Abstract

We give an explicit formula for a right inverse of the trace operator from the Sobolev space H^1^(T) on a triangle T to the trace space H^1/2^(∂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 L~2~(∂T) to H^1/2^(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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)