Adaptive Domain Extension and Adaptive Grids for Unbounded Spherical Elliptic PDEs

Abstract

The problem of approximating the solution to a class of (PDEs) posed on unbounded domains using finite domain approximations is considered. A finite-element method is formulated for the approximation on the finite subregions, and a domain extension strategy that “balances” the finite-element error and domain-truncation error is developed. It is shown that this scheme yields asymptotically optimal finite-element approximation properties to the solution on the unbounded domain as the grid is extended. Error estimates for adaptive refinement and domain truncation are developed.

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