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However, the choice and optimization of multigrid components such as relaxation schemes and grid\u2010transfer operators is crucial to the design of optimally efficient algorithms. It is well known that local Fourier analysis (LFA) is a useful tool to predict and analyze the performance of these components. In this article, we develop a local Fourier analysis of monolithic multigrid methods based on additive Vanka relaxation schemes for mixed finite\u2010element discretizations of the Stokes equations. The analysis offers insight into the choice of \u201cpatches\u201d for the Vanka relaxation, revealing that smaller patches offer more effective convergence per floating point operation. Parameters that minimize the two\u2010grid convergence factor are proposed and numerical experiments are presented to validate the LFA predictions.<\/jats:p>","DOI":"10.1002\/nla.2306","type":"journal-article","created":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T03:46:41Z","timestamp":1592797601000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A local Fourier analysis of additive Vanka relaxation for the Stokes equations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-1241-7060","authenticated-orcid":false,"given":"Patrick E.","family":"Farrell","sequence":"first","affiliation":[{"name":"Mathematical Institute University of Oxford Oxford UK"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3476-2487","authenticated-orcid":false,"given":"Yunhui","family":"He","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics Memorial University of Newfoundland St. John's Newfoundland Canada"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-6364-0684","authenticated-orcid":false,"given":"Scott P.","family":"MacLachlan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics Memorial University of Newfoundland St. John's Newfoundland Canada"}]}],"member":"311","published-online":{"date-parts":[[2020,6,21]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0730031"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/0731070"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2047"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1029\/2009GC002526"},{"key":"e_1_2_7_7_1","doi-asserted-by":"crossref","unstructured":"RudiJ MalossiACI IsaacT et al. 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