Interpolation Operator on negative Sobolev Spaces
Numerical Analysis
2022-12-29 v2 Numerical Analysis
Abstract
We introduce a Scott--Zhang type projection operator mapping to Lagrange elements for arbitrary polynomial order. In addition to the usual properties, this operator is compatible with duals of first order Sobolev spaces. More specifically, it is stable in the corresponding negative norms and allows for optimal rates of convergence. We discuss alternative operators with similar properties. As applications of the operator we prove interpolation error estimates for parabolic problems and smoothen rough right-hand sides in a least squares finite element method.
Cite
@article{arxiv.2112.08515,
title = {Interpolation Operator on negative Sobolev Spaces},
author = {Lars Diening and Johannes Storn and Tabea Tscherpel},
journal= {arXiv preprint arXiv:2112.08515},
year = {2022}
}