Projection geometry and relaxed quasi-orthogonality for inf-sup stable Galerkin methods

arXiv:2609.16265v2 Announce Type: replace Abstract: We give an elementary, coordinate-free proof that uniformly inf-sup stable nested Petrov-Galerkin methods on Hilbert spaces satisfy relaxed general quasi-orthogonality. More precisely, for any window of $N$ consecutive levels, the sum of squared Galerkin increments is bounded by the squared error at the beginning of the window times $N^\sigma$, where $\sigma