Závěrečný komentář editora v recenzním řízení:
This paper presents, probably for the first time, an entirely new line of thought among the mesh adaptivity problems in numerical mathematics. A standard approach to adaptivity is based on the study and estimation of the spatial distribution of discretization errors, with a tacit assumption that the corresponding algebraic system is solved exactly. The latter, however, never occurs in practice. Thus, a natural question that seems to be completely overlooked previously should be asked about the spatial distribution of the errors of algebraic solver. The authors show that those errors dominate in the spatial distribution of the final error and demonstrate, using a kind of backward error analysis, how they can be interpreted in the terms of a change of the basis functions, where the new functions are no longer with finite support. This analysis gives a new vision of adaptivity that must be taken into account in practical strategies. The paper is well written and really opens a new line of research. I recommend publication.