## Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem.(English)Zbl 1340.65298

Summary: In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann 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.

### MSC:

 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J62 Quasilinear elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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### References:

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