Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time

@article{Oliver2014StabilityUG,
title={Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time},
author={M. Oliver and C. Wulff},
journal={Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences},
year={2014},
volume={144},
pages={603-636}
}

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences

We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. We approximate their semiflow by an implicit, A-stable Runge--Kutta discretization in time and a spectral Galerkin truncation in space. We show regularity of the Galerkin-truncated semiflow and its time-discretization on open sets of initial values with bounds that are uniform in the spatial… Expand