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