On Nonlinear Dirichlet-Neumann Algorithms for Jumping Nonlinearities

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in KonferenzbandBeigetragenBegutachtung

Beitragende

  • Heiko Berninger - , Freie Universität (FU) Berlin (Autor:in)
  • Ralf Kornhuber - , Freie Universität (FU) Berlin (Autor:in)
  • Oliver Sander - , Freie Universität (FU) Berlin (Autor:in)

Abstract

We consider a quasilinear elliptic transmission problem where the nonlinearity changes discontinuously across two subdomains. By a reformulation of the problem via a Kirchhoff transformation, we first obtain linear problems on the subdomains together with nonlinear transmission conditions and then a nonlinear Steklov–Poincaré interface equation. We introduce a Dirichlet–Neumann iteration for this problem and prove convergence to a unique solution in one space dimension. Finally we present numerical results in two space dimensions suggesting that the algorithm can be applied successfully in more general cases.

Details

OriginalspracheEnglisch
TitelDomain Decomposition Methods in Science and Engineering XVI
Herausgeber (Verlag)Springer, Berlin [u. a.]
Seiten489-496
PublikationsstatusVeröffentlicht - 2007
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

Scopus 67649327045
ORCID /0000-0003-1093-6374/work/147143092