On norms and traces of the derivatives of the $L^2$-projection error

TL;DR

This paper derives explicit error bounds for the derivatives of the $L^2$ projection of functions in $H^k$ onto polynomial spaces, focusing on traces and norms, with bounds depending on differentiation order and polynomial degree.

Contribution

It provides explicit bounds on the traces and norms of derivatives of the $L^2$ projection, advancing understanding of approximation properties in polynomial spaces.

Findings

Explicit bounds depend on differentiation order and polynomial degree

Bounds apply to traces and norms of derivatives of the projection

Results improve error estimation in polynomial approximation

Abstract

We provide error bounds on the traces and norms of the derivative of the $L^2$ projection of an $H^{k}$ function onto the space of polynomials of degree $\leq p$. The bounds are explicit in the order of differentiation and the polynomial degree $p$.