An extension theorem for polynomials on triangles

We present an extension theorem for polynomial functions that proves a quasi-optimal bound for a lifting from L ² on edges onto a fractional-order Sobolev space on triangles. The extension is such that it can be further extended continuously by zero within the trace space of H ¹. Such an extension result is critical for the analysis of non-overlapping domain decomposition techniques applied to the p-and hp-versions of the finite and boundary element methods for elliptic problems of second order in three dimensions.