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Math. Anal."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The Laplace\u2013Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle deformation). In particular, the Hodge decomposition of vector fields tangent to a surface can be computed by solving a sequence of Laplace\u2013Beltrami problems. Such decompositions are very important in magnetostatic calculations and in various plasma and fluid flow problems. In this work we develop [Formula: see text]-invertibility theory for the Laplace\u2013Beltrami operator on piecewise smooth surfaces, extending earlier weak formulations and integral equation approaches on smooth surfaces. Furthermore, we reformulate the weak form of the problem as an interface problem with continuity conditions across edges of adjacent piecewise smooth panels of the surface. We then provide high-order numerical examples along surfaces of revolution to support our analysis and discuss numerical extensions to general surfaces embedded in three dimensions.<\/jats:p>","DOI":"10.1137\/22m1538454","type":"journal-article","created":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T04:06:13Z","timestamp":1699416373000},"page":"7575-7615","source":"Crossref","is-referenced-by-count":2,"title":["An Interface Formulation of the Laplace\u2013Beltrami Problem on Piecewise Smooth Surfaces"],"prefix":"10.1137","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2201-5716","authenticated-orcid":true,"given":"Tristan","family":"Goodwill","sequence":"first","affiliation":[{"name":"Courant Institute, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2724-215X","authenticated-orcid":true,"given":"Michael","family":"O\u2019Neil","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,8]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/42.796283"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.08.022"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1142\/S021820251440003X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/bs.hna.2019.06.002"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/17M1163311"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.03.002"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1476(20010110)24:1<31::AID-MMA193>3.0.CO;2-X"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100372"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0407-z"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drv068"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2012.2233456"},{"key":"ref12","volume-title":"Theory of Ordinary Differential Equations","author":"Coddington E. 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