Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements
Numerical Analysis
2026-04-24 v1 Numerical Analysis
Abstract
A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framework allows for non-selfadjoint problems and extends the existing verification theory to nonconforming discretisations. A key ingredient is a guaranteed lower bound on the continuous inf-sup constant from a quasi-optimal nonconforming discretisation that enables a novel a priori error estimator. All quantities are obtained by post-processing a single discretisation; convergence rates are proved. The theory is applied to a fourth-order formulation of the stationary two-dimensional Navier--Stokes equations and illustrated by numerical experiments.
Keywords
Cite
@article{arxiv.2604.21887,
title = {Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements},
author = {Benedikt Gräßle},
journal= {arXiv preprint arXiv:2604.21887},
year = {2026}
}