Operator splitting for abstract Cauchy problems with dynamical boundary condition
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.13503
- arXiv:
- arXiv:2004.13503
- Bibcode:
- 2020arXiv200413503C
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematics - Functional Analysis;
- 47D06;
- 47N40;
- 34G10;
- 65J08;
- 65M12;
- 65M15