We consider a quasilinear elliptic transmission problem where the nonlinearity changes discontinuously across two subdomains. By a reformulation of the problem via a Kirchho. 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.
CITATION STYLE
Berninger, H., Kornhuber, R., & Sander, O. (2007). On Nonlinear Dirichlet-Neumann Algorithms for Jumping Nonlinearities. Lecture Notes in Computational Science and Engineering, 55, 489–496. https://doi.org/10.1007/978-3-540-34469-8_61
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