Three-dimensional superconvergent gradient recovery on tetrahedral meshes

Jie Chen*, Zhangxin Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have O(h1+ɑ)(ɑ ≈ 0.5) superconvergence in the l2 norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method.

Original languageEnglish
Pages (from-to)819-838
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
Publication statusPublished - 23 Nov 2016
Externally publishedYes


  • centroidal Voronoi Delaunay tessellation
  • finite element methods
  • modified superconvergence patch recovery
  • superconvergence

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