The Trotter-Kato theorem and approximation of PDEs

Abstract. We present formulations of the Trotter-Kato theorem for approximation of linear C0-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.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Kazufumi Ito, Franz Kappel
• Keywords: MOC 1998, Numerical Approximations, Order Hyperbolic Equation, Wave Equation