Finite element methods for surface PDEs*

By Gerhard Dziuk, Charles M. Elliott. Acta Numerica, 2013

659 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f184460e5ad21fa74978afbce56159e4e9e61f8d

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Modelling fluid deformable surfaces with an emphasis on biological interfaces (2018, methodology): “Even if the interaction with a bulk fluid is not considered, the interfacial velocity can be extended to a tubular neighbourhood in 3D around the interface to find the governing equations, which can be shown to be independent of the extension (Dziuk & Elliott 2007, 2013).”
Analysis of finite element methods for vector Laplacians on surfaces (2016, positive): “Most of the research is, however, focused on problems with scalar unknowns, see the recent review article [6] and the references therein, which simplifies the differential calculus since the covariant derivative of a vector field, or more generally a tensor field, is not needed.”
Stream function formulation of surface Stokes equations (2018, background): “, the review paper [13] for scalar surface PDEs and [21, 36, 37, 29, 30, 38] for surface (Navier-)Stokes equations.”
A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015, methodology): “For the first, we propose a discretization which is semi-implicit in time and which is based on surface finite elements in space [14, 15].”
Finite element methods for the Laplace–Beltrami operator (2020, background): “iorcalculusformulations[Ben84, HS12, CD16, FFF16]. A posteriori error estimation and adaptivity have been studied in [DD07, WCH10, BCMN13, DM16, BCM+16, BD19]. Finally, we refer to the survey article [DE13]. In many applications in which surface PDEs are to be solved, a background volume (bulk) mesh”