On surface meshes induced by level set functions
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by
Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
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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1301.3745v1
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