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We derive general abstract estimates based on the theory of functional <jats:italic>a posteriori<\/jats:italic> error estimates, for which guaranteed upper bounds for the primal and dual variables and two-sided bounds for the primal\u2013dual pair are obtained. We improve on the abstract results obtained with the functional approach by proposing four different ways of estimating the residual errors based on the extent the approximate solution has conservation properties, i.e., (1) no conservation, (2) subdomain conservation, (3) grid-level conservation, and (4) exact conservation. This treatment results in sharper and fully computable estimates when mass is conserved either at the grid level or exactly, with a comparable structure to those obtained from grid-based <jats:italic>a posteriori<\/jats:italic> techniques. We demonstrate the practical effectiveness of our theoretical results through numerical experiments using four different discretization methods for synthetic problems and applications based on benchmarks of flow in fractured porous media.<\/jats:p>","DOI":"10.1515\/jnma-2022-0038","type":"journal-article","created":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T10:01:06Z","timestamp":1666260066000},"page":"247-280","source":"Crossref","is-referenced-by-count":4,"title":["<i>A posteriori<\/i> error estimates for hierarchical mixed-dimensional elliptic equations"],"prefix":"10.1515","volume":"31","author":[{"given":"Jhabriel","family":"Varela","sequence":"first","affiliation":[{"name":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"}]},{"given":"Elyes","family":"Ahmed","sequence":"additional","affiliation":[{"name":"SINTEF Digital , Mathematics and Cybernetics , Oslo , Norway"}]},{"given":"Eirik","family":"Keilegavlen","sequence":"additional","affiliation":[{"name":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"}]},{"given":"Jan M.","family":"Nordbotten","sequence":"additional","affiliation":[{"name":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"}]},{"given":"Florin A.","family":"Radu","sequence":"additional","affiliation":[{"name":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"}]}],"member":"374","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"2023120515545641323_j_jnma-2022-0038_ref_001","unstructured":"I. 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