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arXiv · 1703.07077

Cut Finite Element Methods for Elliptic Problems on Multipatch Parametric Surfaces

Tobias Jonsson·Mats G. Larson·Karl Larsson
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Abstract

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.

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Tobias Jonsson, Mats G. Larson, Karl Larsson. 2017-06-22. Cut Finite Element Methods for Elliptic Problems on Multipatch Parametric Surfaces. https://doi.org/10.1016/j.cma.2017.06.018

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