Operator Splitting for Abstract Cauchy Problems with Dynamical Boundary Conditions

Csomós, Petra and Ehrhardt, Matthias and Farkas, Bálint (2020) Operator Splitting for Abstract Cauchy Problems with Dynamical Boundary Conditions. OPERATORS AND MATRICES. ISSN 1846-3886 (In Press)

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Abstract

In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a “boundary type” extra condition for the other one. The theory of one-sided coupled operator matrices provides an excellent framework to study the well-posedness of such problems. We show that with this machinery even operator splitting methods can be treated conveniently and rather efficiently. We consider three specific examples: the Lie (sequential), the Strang and the weighted splitting, and prove the convergence of these methods along with error bounds under fairly general assumptions.

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