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We demonstrate the numerical behavior of the method by performing numerical tests for the solid-body rotation benchmark in a unit square and for a transport problem along a curve implicitly prescribed by a level set function. Extension of the proposed method to higher dimensions is straightforward and easily realizable.<\/jats:p>","DOI":"10.1515\/jnma-2018-0097","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T09:04:15Z","timestamp":1561712655000},"page":"253-269","source":"Crossref","is-referenced-by-count":12,"title":["A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds"],"prefix":"10.1515","volume":"27","author":[{"given":"Andriy","family":"Sokolov","sequence":"first","affiliation":[{"name":"Institute for Applied Mathematics , TU Dortmund , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oleg","family":"Davydov","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Giessen , Giessen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitri","family":"Kuzmin","sequence":"additional","affiliation":[{"name":"Institute for Applied Mathematics , TU Dortmund , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Westermann","sequence":"additional","affiliation":[{"name":"Institute for Applied Mathematics , TU Dortmund , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Turek","sequence":"additional","affiliation":[{"name":"Institute for Applied Mathematics , TU Dortmund , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,6,26]]},"reference":[{"key":"2024082322171405911_j_jnma-2018-0097_ref_001_w2aab3b7b1b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"M. 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