Numerical Method for Solving Elliptic Boundary Value Problems in Unbounded Domains

摘要

A numerical method for solving elliptic boundary value problems in unbounded domains is described. An artificial boundary near infinity, say a sphere GAMMA/sub R/ of large radius R, and an approximate local boundary condition on GAMMA/sub R/ are introduced. A finite element method is then employed to discretize this approximate problem. Since R must be large in order to estimate the error due to the artificial boundary, the resulting system of linear equations is usually quite large. A description is given on how to reduce the number of linear equations to the asymptotically optimal amount, while optimal error estimates and the sparseness of the matrix are preserved, by grading the mesh systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. Some numerical results are given. 1 table. (ERA citation 05:033155)