Functional A Posteriori Error Estimates for Elliptic Problems in Exterior Domains
Provides rigorous error control for numerical solutions of elliptic PDEs in exterior domains, which is important for applications in physics and engineering, though the extension is incremental.
This paper derives computable and guaranteed upper bounds for the error between exact and approximate solutions of elliptic problems in exterior domains, extending functional-type error estimates from bounded to unbounded domains.
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.