Geodesic
Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem
Applications of Mathematics, Tome 59 (2014) no. 3, pp. 285-301.

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In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence. Moreover, the convergence rate is obtained in detail for a typical domain. Finally, some numerical examples are presented to illustrate the feasibility of the method.
DOI : 10.1007/s10492-014-0055-5
Classification : 35J62, 35J65, 65N30, 65N55
Keywords: quasilinear elliptic equation; domain decomposition method; natural integral equation 
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Liu, Baoqing; Du, Qikui. Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem. Applications of Mathematics, Tome 59 (2014) no. 3, pp. 285-301. doi : 10.1007/s10492-014-0055-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0055-5/

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