Explicit polynomial preserving trace liftings on a triangle

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)