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}
}
  • M. Oliver, C. Wulff
  • Published 2014
  • Mathematics
  • 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
3 Citations

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