Operator splitting for abstract Cauchy problems with dynamical boundary condition
Analysis of PDEs
2021-05-21 v2 Functional Analysis
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.
Cite
@article{arxiv.2004.13503,
title = {Operator splitting for abstract Cauchy problems with dynamical boundary condition},
author = {Petra Csomós and Matthias Ehrhardt and Bálint Farkas},
journal= {arXiv preprint arXiv:2004.13503},
year = {2021}
}