Trace finite element methods for PDEs on surfaces. (English) Zbl 1448.65245
Bordas, Stéphane P. A. (ed.) et al., Geometrically unfitted finite element methods and applications. Proceedings of the UCL workshop, London, UK, January, 6–8, 2016. Cham: Springer. Lect. Notes Comput. Sci. Eng. 121, 211-258 (2017).
Summary: In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of background surface-independent finite element functions are used to approximate the solution of a PDE on a surface. We treat equations on steady and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in detail. We review the error analysis and algebraic properties of the method. The paper navigates through the known variants of the TraceFEM and the literature on the subject.
For the entire collection see [Zbl 1392.65006].
For the entire collection see [Zbl 1392.65006].
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35R01 | PDEs on manifolds |
