The Trotter-Kato theorem and approximation of PDEs

Ito, Kazufumi; Kappel, Franz

doi:10.1090/S0025-5718-98-00915-6

The Trotter-Kato theorem and approximation of PDEs
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by Kazufumi Ito and Franz Kappel PDF

Math. Comp. 67 (1998), 21-44 Request permission

Abstract:

We present formulations of the Trotter-Kato theorem for approximation of linear C${}_0$-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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