Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains

TL;DR

This paper develops functional a posteriori error estimates that provide guaranteed upper bounds for the difference between exact and approximate solutions of elliptic boundary value problems in exterior domains, applicable to any approximation method.

Contribution

It extends the derivation of functional a posteriori error estimates to exterior domain elliptic problems, independent of specific approximation techniques.

Findings

Derivation of guaranteed upper bounds for exterior domain problems

Estimates applicable to any approximation method in energy space

Extension of functional error estimates from bounded to unbounded domains

Abstract

This paper is concerned with the derivation of computable and guaranteed upper bounds of the difference between the exact and the approximate solution of an exterior domain boundary value problem for a linear elliptic equation. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the estimates derived in the paper at hand are applicable to any approximate solution that belongs to the corresponding energy space. Such estimates (also called error majorants of the functional type) have been derived earlier for problems in bounded domains.