Exact artificial boundary conditions for quasilinear elliptic equations in unbounded domains

Abstract

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