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  • Autor
    • Carl, Wolfgang
    • Wallner, Johannes
  • TitelVariational Laplacians for semidiscrete surfaces
  • Datei
  • DOI10.1007/s10444-016-9472-1
  • Persistent Identifier
  • Erschienen inAdvances in Computational Mathematics
  • Band42
  • Erscheinungsjahr2016
  • Heft6
  • Seiten1491-1509
  • ISSN1572-9044
  • ZugriffsrechteCC-BY
  • Download Statistik307
  • Peer ReviewJa
  • AbstractWe study a Laplace operator on semidiscrete surfaces that is defined by variation of the Dirichlet energy functional. We show existence and its relation to the mean curvature normal, which is itself defined via variation of area. We establish several core properties like linear precision (closely related to the mean curvature of flat surfaces), and pointwise convergence. It is interesting to observe how a certain freedom in choosing area measures yields different kinds of Laplacians: it turns out that using as a measure a simple numerical integration rule yields a Laplacian previously studied as the pointwise limit of geometrically meaningful Laplacians on polygonal meshes.