@inproceedings{e8f324ff5c0a4ecf81a4ba82bc65df8b,
title = "Operator semigroups for convergence analysis",
abstract = "The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems of Trotter and Kato, Lax, and Chernoff. We also list some of their most important applications.",
keywords = "Chernoff{\textquoteright}s theorem, Convergence analysis, Lax equivalence theorem, Numerical analysis, Operator semigroups, Trotter-kato approximation theorem",
author = "Petra Csom{\'o}s and Istv{\'a}n Farag{\'o} and Imre Fekete",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 6th International Conference on Finite Difference Methods, FDM 2014 ; Conference date: 18-06-2014 Through 23-06-2014",
year = "2015",
doi = "10.1007/978-3-319-20239-6_4",
language = "English",
isbn = "9783319202389",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "38--49",
editor = "Istvan Farago and Lubin Vulkov and Ivan Dimov",
booktitle = "Finite Difference Methods, Theory and Applications - 6th International Conference, FDM 2014, Revised Selected Papers",
}