Communications in Mathematical Sciences

Volume 6 (2008)

Number 1

Exact artificial boundary conditions for quasilinear elliptic equations in unbounded domains

Pages: 71 – 82



Houde Han

Zhongyi Huang

Dongsheng Yin


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


quasilinear elliptic equation, unbounded domain, artificial boundary condition

2010 Mathematics Subject Classification

35J65, 65N30

Published 1 January 2008