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Lie splitting on polygonal domains
Author(s) -
Ostermann Alexander,
Schratz Katharina,
Spielberger Georg
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110382
Subject(s) - convergence (economics) , regular polygon , reduction (mathematics) , mathematics , order (exchange) , mathematical analysis , pure mathematics , geometry , economics , finance , economic growth
In this short note, we discuss the convergence properties of splitting methods for the time integration of parabolic evolution equations. Through numerical experiments we show that the Lie splitting method suffers from an order reduction on non‐convex polygonal domains. An in‐depth study of the local error allows us to explain this behavior and to understand the improved convergence properties of a related scheme, the Douglas‐Rachford method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)