Dimension splitting for evolution equations

Authors:
Eskil Hansen;Alexander Ostermann
Affiliations:
Universität Innsbruck, Institut für Mathematik, Technikerstraße 13, A-6020, Innsbruck, Austria;Universität Innsbruck, Institut für Mathematik, Technikerstraße 13, A-6020, Innsbruck, Austria
Venue:
Numerische Mathematik
Year:
2008

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Abstract

In this paper, we are concerned with splitting methods for the time integration of abstract evolution equations. We introduce an analytic framework which allows us to prove optimal convergence orders for various splitting methods, including the Lie and Peaceman–Rachford splittings. Our setting is applicable for a wide variety of linear equations and their dimension splittings. In particular, we analyze parabolic problems with Dirichlet boundary conditions, as well as degenerate equations on bounded domains. We further illustrate our theoretical results with a set of numerical experiments.