2013/01/16 by Maxim A. Olshanskii, Olshanskii, Maxim A., Arnold Reusken +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1301.3745
openalex publication_date 2013/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in ℝ3 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 P1 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.