On surface meshes induced by level set functions release_xyl3kejb7zfgfir5rorr2c26ai [as of editgroup_gsiatvwuajcl5pzby6mla42lru]

by Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu

Released as a article .

2013  

Abstract

The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in R^3 is a piecewise-planar hyper-surface. We prove that if a family of consistent tetrahedral subdivions satisfies the minimum angle condition, then after a simple postprocessing this zero level set becomes a consistent surface triangulation which satisfies the maximum angle condition. We treat an application of this result to the numerical solution of PDEs posed on surfaces, using a P_1 finite element space on such a surface triangulation. For this finite element space we derive optimal interpolation error bounds. We prove that the diagonally scaled mass matrix is well-conditioned, uniformly with respect to h. Furthermore, the issue of conditioning of the stiffness matrix is addressed.
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Type  article
Stage   submitted
Date   2013-01-16
Version   v1
Language   en ?
arXiv  1301.3745v1
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