Dimension splitting for evolution equations |
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Authors: | Eskil Hansen Alexander Ostermann |
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Institution: | 1. Institut für Mathematik, Universit?t Innsbruck, Technikerstra?e 13, A-6020, Innsbruck, Austria
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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.
This work was supported by the Austrian Science Fund under grant M961-N13. |
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Keywords: | 65M12 65J10 65L05 47N40 |
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