This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between exact and approximate solutions of a boundary value problem for static Maxwell equations. Our analysis is based upon purely functional argumentation and does not invoke specific properties of the approximation method. For this reason, 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. Bibliography: 24 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 370, 2009, pp. 94–110.
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Pauly, D., Repin, S. Two-sided a posteriori error bounds for electro-magnetostatic problems. J Math Sci 166, 53–62 (2010). https://doi.org/10.1007/s10958-010-9844-x
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DOI: https://doi.org/10.1007/s10958-010-9844-x