Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains

Details Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains

2011-05-20

arxiv.org/abs/1105.4101v1

Problemy Matematicheskogo Analiza, 42, (2009), 83-94 & Journal of Mathematical Sciences (Springer New York), 162 (3), (2009),

Mathematics

Analysis of PDEs

Key Words: A posteriori error estimates of functional type, elliptic boundary value problems in exterior domains

Scientific paper

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.

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