Berninger, H. and Kornhuber, R. and Sander, O. (2011) Convergence behaviour of DirichletNeumann and Robin methods for a nonlinear transmission problem. In: Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, 78 . Springer Berlin Heidelberg, pp. 8798. ISBN 9783642113031

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Official URL: http://dx.doi.org/10.1007/9783642113048_8
Abstract
We investigate Dirichlet–Neumann and Robin methods for a quasilinear elliptic transmission problem in which the nonlinearity changes discontinuously across two subdomains. In one space dimension, we obtain convergence theorems by extending known results from the linear case. They hold both on the continuous and on the discrete level. From the proofs one can infer meshindependence of the convergence rates for the Dirichlet–Neumann method, but not for the Robin method. In two space dimensions, we consider numerical examples which demonstrate that the theoretical results might be extended to higher dimensions. Moreover, we investigate the asymptotic convergence behaviour for fine mesh sizes quantitatively. We observe a good agreement with many known linear results, which is remarkable in view of the nonlinear character of the problem.
Item Type:  Book Section 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1797 
Deposited By:  Ekaterina Engel 
Deposited On:  18 Feb 2016 09:37 
Last Modified:  03 Mar 2017 14:41 
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