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A Lagrange multiplier space that consists of continuous piecewise polynomials with respect to the boundary partition is introduced to enforce boundary conditions and to mitigate the lack of pressure-robustness. We prove several inf-sup conditions, leading to the well-posedness of the method. In addition, we show that the method converges with optimal order and the velocity approximation is divergence-free.<\/jats:p>","DOI":"10.1515\/jnma-2021-0125","type":"journal-article","created":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T21:38:21Z","timestamp":1649972301000},"page":"105-123","source":"Crossref","is-referenced-by-count":4,"title":["A divergence-free finite element method for the Stokes problem with boundary correction"],"prefix":"10.1515","volume":"31","author":[{"given":"Haoran","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Neilan","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Baris Otus","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,4,14]]},"reference":[{"key":"2023060911023285070_j_jnma-2021-0125_ref_001","unstructured":"D. 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