Convergence Behaviour of Dirichlet–Neumann and Robin Methods for a Nonlinear Transmission Problem

Research output: Contribution to book/conference proceedings/anthology/reportConference contributionContributedpeer-review

Contributors

  • Heiko Berninger - , Free University of Berlin (Author)
  • Ralf Kornhuber - , Free University of Berlin (Author)
  • Oliver Sander - , Free University of Berlin (Author)

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 mesh-independence 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.

Details

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XIX
PublisherSpringer, Berlin [u. a.]
Pages87-98
ISBN (electronic)978-3-642-11304-8
ISBN (print)978-3-642-11303-1
Publication statusPublished - 2011
Peer-reviewedYes
Externally publishedYes

External IDs

Scopus 78651569785
ORCID /0000-0003-1093-6374/work/146644828