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These schemes are the algebraic flux correction (AFC) scheme with the Kuzmin limiter, the AFC scheme with the Barrenechea-John-Knobloch limiter, and the recently proposed monotone upwind\u2013type algebraically stabilized method. Both conforming closure of the refined grids and grids with hanging vertices are considered. A nonstandard algorithmic step becomes necessary before these schemes can be applied on grids with hanging vertices. The assessment of the schemes is performed with respect to the satisfaction of the global discrete maximum principle, the accuracy, e.g., smearing of layers, and the efficiency in solving the corresponding nonlinear problems.<\/jats:p>","DOI":"10.1137\/21m1466360","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T09:44:37Z","timestamp":1691055877000},"page":"B564-B589","source":"Crossref","is-referenced-by-count":9,"title":["Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations"],"prefix":"10.1137","volume":"45","author":[{"given":"Abhinav","family":"Jha","sequence":"first","affiliation":[{"name":"Institute of Applied Analysis and Numerical Simulation, Universit\u00e4t Stuttgart, 70569, Stuttgart, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2711-4409","authenticated-orcid":true,"given":"Volker","family":"John","sequence":"additional","affiliation":[{"name":"Weierstrass Institute for Applied Analysis and Stochastics (WIAS), 10117 Berlin, Germany, and Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2709-5882","authenticated-orcid":true,"given":"Petr","family":"Knobloch","sequence":"additional","affiliation":[{"name":"Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 8, 18675, Czech Republic."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,8,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/080725945"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1092763"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2011.08.012"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2017.03.032"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2014.12.006"},{"key":"ref6","series-title":"IMACS Trans. 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