Convergence analysis on the Gibou-Min method for the Hodge projection

Gangjoon Yoon, Jea Hyun Park, Chohong Min

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2 Scopus citations


The Hodge projection of a vector field is the divergence-free component of its Helmholtz decomposition. In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. In the decomposition by the Gibou-Min method, an important L2-orthogonality holds between the gradient field and the solenoidal field, which is similar to the continuous Hodge decomposition. Using the orthogonality, we present a novel analysis which shows that the convergence order is 1.5 in the L2-norm for approximating the divergence-free vector field. Numerical results are presented to validate our analyses.

Original languageEnglish
Pages (from-to)1211-1220
Number of pages10
JournalCommunications in Mathematical Sciences
Issue number5
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 International Press.


  • Finite volume method
  • Gibou-Min
  • Hodge projection
  • Poisson equation


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