The Trotter-Kato theorem and approximation of PDEs
Open Access
- 1 January 1998
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 67 (221) , 21-44
- https://doi.org/10.1090/s0025-5718-98-00915-6
Abstract
We present formulations of the Trotter-Kato theorem for approximation of linear C 0 {}_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.Keywords
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