Two-Sided A Posteriori Error Bounds for Electro-Magneto Static Problems

TL;DR

This paper develops computable, guaranteed upper and lower bounds for the error in approximate solutions of static Maxwell equations, applicable to any approximation method within the energy space.

Contribution

It introduces a functional approach to derive two-sided a posteriori error bounds for electro-magneto static problems, independent of specific approximation techniques.

Findings

Derivation of guaranteed error bounds for static Maxwell problems

Applicable to any approximation within the energy space

Extends functional error estimation methods to electromagneto static problems

Abstract

This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. 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 elliptic problems.