The Trotter-Kato theorem and approximation of PDEs

@article{Ito1998TheTT,
  title={The Trotter-Kato theorem and approximation of PDEs},
  author={Kazufumi Ito and Franz Kappel},
  journal={Math. Comput.},
  year={1998},
  volume={67},
  pages={21-44}
}
We present formulations of the Trotter-Kato theorem for approximation of linear C0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples. 
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