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The method employs parametric <jats:bold>P<\/jats:bold>\n                  <jats:sub>\n                     <jats:italic>k<\/jats:italic>\n                  <\/jats:sub>-<jats:italic>P<\/jats:italic>\n                  <jats:sub>\n                     <jats:italic>k<\/jats:italic>\u22121<\/jats:sub> finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin\u2013Helmholtz instability problem on the unit sphere.<\/jats:p>","DOI":"10.1515\/jnma-2020-0017","type":"journal-article","created":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T19:46:54Z","timestamp":1601927214000},"page":"245-267","source":"Crossref","is-referenced-by-count":22,"title":["Error analysis of higher order Trace Finite Element Methods for the surface Stokes equation"],"prefix":"10.1515","volume":"29","author":[{"given":"Thomas","family":"Jankuhn","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Geometrie und Praktische Mathematik , RWTH-Aachen University , D-52056 , Aachen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxim A.","family":"Olshanskii","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Houston , Houston , Texas 77204 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnold","family":"Reusken","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Geometrie und Praktische Mathematik , RWTH-Aachen University , D-52056 , Aachen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Zhiliakov","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Houston , Houston , Texas 77204 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2021,9,25]]},"reference":[{"key":"2021092820582048206_j_jnma-2020-0017_ref_001","doi-asserted-by":"crossref","unstructured":"M. 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