Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 324, Issue -, Pages 366-394Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.06.018
Keywords
Cut finite elements; Fictitious domain; Nitsche's method; A priori error estimates; Multipatch surface; Laplace-Beltrami operator
Funding
- Swedish Foundation for Strategic Research [AM13-0029]
- Swedish Research Council [2013-4708]
- Swedish strategic research programme eSSENCE
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We develop a finite element method for the Laplace-Beltrami operator on a surface described by a set of patchwise parametrizations. The patches provide a partition of the surface and each patch is the image by a diffeomorphism of a subdomain of the unit square which is bounded by a number of smooth trim curves. A patchwise tensor product mesh is constructed by using a structured mesh in the reference domain. Since the patches are trimmed we obtain cut elements in the vicinity of the interfaces. We discretize the Laplace-Beltrami operator using a cut finite element method that utilizes Nitsche's method to enforce continuity at the interfaces and a consistent stabilization term to handle the cut elements. Several quantities in the method are conveniently computed in the reference domain where the mappings impose a Riemannian metric. We derive a priori estimates in the energy and L-2 norm and also present several numerical examples confirming our theoretical results. (C) 2017 Elsevier B.V. All rights reserved.
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