A nodal integral method for quadrilateral elements

Erfan G. Nezami, Suneet Singh, Nahil Sobh, Rizwan Uddin

Research output: Contribution to journalArticlepeer-review


Nodal integral methods (NIMs) have been developed and successfully used to numerically solve several problems in science and engineering. The fact that accurate solutions can be obtained on relatively coarse mesh sizes, makes NIMs a powerful numerical scheme to solve partial differential equations. However, transverse integration procedure, a step required in the NIMs, limits its applications to brick-like cells, and thus hinders its application to complex geometries. To fully exploit the potential of this powerful approach, abovementioned limitation is relaxed in this work by first using algebraic transformation to map the arbitrarily shaped quadrilaterals, used to mesh the arbitrarily shaped domain, into rectangles. The governing equations are also transformed. The transformed equations are then solved using the standard NIM. The scheme is developed for the Poisson equation as well as for the time-dependent convection-diffusion equation. The approach developed here is validated by solving several benchmark problems. Results show that the NIM coupled with an algebraic transformation retains the coarse mesh properties of the original NIM.

Original languageEnglish (US)
Pages (from-to)144-164
Number of pages21
JournalInternational Journal for Numerical Methods in Fluids
Issue number2
StatePublished - Sep 20 2009


  • Algebraic transformation
  • Coarse mesh methods
  • Convection-diffusion
  • Irregular-shaped elements
  • Nodal integralmethod
  • Poissonequation

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics
  • Computer Science Applications
  • Computational Mechanics


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