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Zbl 1168.65412
Han, Houde; Huang, Zhongyi; Yin, Dongsheng
Exact artificial boundary conditions for quasilinear elliptic equations in unbounded domains. (English)
[J] Commun. Math. Sci. 6, No. 1, 71-82 (2008). ISSN 1539-6746

Summary: To study the numerical solutions of quasilinear elliptic equations on unbounded domains in two or three dimensional cases, we introduce a circular or spherical artificial boundary. Based on the Kirchhoff transformation and the Fourier series expansion, the exact artificial boundary condition and a series of its approximations of the given quasilinear elliptic problem are presented. Then the original problem is equivalently or approximately reduced to a bounded computational domain. The well-posedness of the reduced problems are proved and the convergence results of our numerical solutions on bounded computational domain are given

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35J65 (Nonlinear) BVP for (non)linear elliptic equations

Keywords: quasilinear elliptic equation; unbounded domain; artificial boundary condition; numerical examples; Kirchhoff transformation; Fourier series expansion; convergence

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Zentralblatt MATH Berlin [Germany]