E28

We introduce a Scott–Zhang type projection operator mapping to Lagrange elements for any polynomial order. Additionally to the usual properties, this operator is compatible with negative Sobolev norms. More specifically, it is stable in these weaker norms and leads to optimal rates of convergence. We discuss alternative operators and apply the operator to prove interpolation error estimates for parabolic problems. This is joint work with Tabea Tscherpel and Johannes Storn.

Lars Diening