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Explicit Polynomial Preserving Trace Liftings on a Triangle by Mark Ainsworth; Leszek Demkowicz is a Mathematics article available to read on EtoBox.

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## 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)

Who reads Explicit Polynomial Preserving Trace Liftings on a Triangle?

Author

Mark Ainsworth; Leszek Demkowicz

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)