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The zero level set of a piecewise-affine function with respect to aconsistent tetrahedral subdivision of a domain in $\mathbb{R}^3$ is apiecewise-planar hyper-surface. We prove that if a family of consistenttetrahedral subdivions satisfies the minimum angle condition, then after asimple postprocessing this zero level set becomes a consistent surfacetriangulation which satisfies the maximum angle condition. We treat anapplication 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 thisfinite element space we derive optimal interpolation error bounds. We provethat the diagonally scaled mass matrix is well-conditioned, uniformly withrespect to $h$. Furthermore, the issue of conditioning of the stiffness matrixis addressed.

On surface meshes induced by level set functions