An Iterative Substructuring Method for div-stable Finite Element Approximations of the Oseen Problem |
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Authors: | F C Otto G Lube L Müller |
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Affiliation: | Universit?t G?ttingen, Fakult?t für Mathematik, NAM D-37083 G?ttingen Germany e-mail: lube@math.uni-goettingen.de, DE
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Abstract: | We apply an iterative substructuring algorithm with transmission conditions of Robin–Robin type to the discretized Oseen
problem appearing as a linearized variant of the incompressible Navier–Stokes equations. Here we consider finite element approximations
using velocity/pressure pairs which satisfy the Babuška–Brezzi stability condition. After proving well-posedness and strong
convergence of the method, we derive an a-posteriori error estimate which controls convergence of the discrete subdomain solutions
to the global discrete solution by measuring the jumps of the velocities at the interface. Additionally we obtain information
how to design a parameter of the Robin interface condition which essentially influences the convergence speed. Numerical experiments
confirm the theoretical results and the applicability of the method.
Received February 18, 2000; revised February 21, 2001 |
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Keywords: | AMS Subject Classifications: 65N55 76M10 |
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