Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

T. P. Fries*, D. Schöllhammer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

Original languageEnglish
Pages (from-to)270-297
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Nov 2017


  • Higher-order FEM
  • Level-set method
  • Manifold
  • Surface PDEs

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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