Minimal surface computation using a finite element method on an embedded surface. (21st April 2015)

• Record Type: Journal Article
• Authors: Cenanovic, Mirza; Hansbo, Peter; Larson, Mats G.; Dolbow, John; Farhat, Charbel; Harari, Isaac; Lew, Adrian
• Is Part Of: International journal for numerical methods in engineering. Volume 104:Number 7(2015)
• Page Start: 502
• Page End: 512
• Publication Date: 2015-04-21
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4892
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4892-abs-0001"> <title>Summary</title> <p id="nme4892-para-0001">We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace–Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three‐dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method. Copyright © 2015 John Wiley &amp; Sons, Ltd.</p> </abstract>