Lehrenfeld, Christoph

[["dc.bibliographiccitation.firstpage","2503"],["dc.bibliographiccitation.issue","11"],["dc.bibliographiccitation.journal","International Journal for Numerical Methods in Engineering"],["dc.bibliographiccitation.lastpage","2533"],["dc.bibliographiccitation.volume","121"],["dc.contributor.author","Lederer, Philip L."],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Schöberl, Joachim"],["dc.date.accessioned","2020-03-02T14:38:53Z"],["dc.date.available","2020-03-02T14:38:53Z"],["dc.date.issued","2020-02-18"],["dc.description.abstract","In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning $H^1$-conformity allows us to construct finite elements which are -- due to an application of the Piola transformation -- exactly tangential. To reintroduce continuity (in a weak sense) we make use of (hybrid) discontinuous Galerkin techniques. To further improve this approach, $H(\\operatorname{div}_{\\Gamma})$-conforming finite elements can be used to obtain exactly divergence-free velocity solutions. We present several new finite element discretizations. On a number of numerical examples we examine and compare their qualitative properties and accuracy."],["dc.description.sponsorship","Austrian Science Fund http://dx.doi.org/10.13039/501100002428"],["dc.identifier.arxiv","1909.06229v2"],["dc.identifier.doi","10.1002/nme.6317"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63041"],["dc.language.iso","en"],["dc.notes.intern","DeepGreen Import"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Divergence-free tangential finite element methods for incompressible flows on surfaces"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]