Operator Semigroups for Convergence Analysis
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.
KeywordsNumerical analysis Operator semigroups Convergence analysis Trotter–kato approximation theorem Lax equivalence theorem Chernoff’s theorem
P. Csomós and I. Faragó kindly acknowledge the support of the bilateral Hungarian-Austrian Science and Technology program TET_10-1-2011-0728. I. Fekete was supported by the European Union and the State of Hungary, co-financed by the European Social Fund witihin the framework of TÁMOP-4.2.4.A/2-11/1-2012-0001 ‘National Program of Excellence’–convergence program.
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