The Trotter-Kato theorem and approximation of PDEs.(English)Zbl 0893.47025

Summary: 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.

MSC:

 47D06 One-parameter semigroups and linear evolution equations 47H05 Monotone operators and generalizations 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 35L99 Hyperbolic equations and hyperbolic systems 65J10 Numerical solutions to equations with linear operators
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