A Projection Method for the Conservative Discretizations of Parabolic Partial Differential Equations

Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review


We present a projection method for the conservative discretizations of parabolic partial differential equations. When we solve a system of discrete equations arising from the finite difference discretization of the PDE, we can use iterative algorithms such as conjugate gradient, generalized minimum residual, and multigrid methods. An iterative method is a numerical approach that generates a sequence of improved approximate solutions for a system of equations. We repeat the iterative algorithm until a numerical solution is within a specified tolerance. Therefore, even though the discretization is conservative, the actual numerical solution obtained from an iterative method is not conservative. We propose a simple projection method which projects the non-conservative numerical solution into a conservative one by using the original scheme. Numerical experiments demonstrate the proposed scheme does not degrade the accuracy of the original numerical scheme and it preserves the conservative quantity within rounding errors.

Original languageEnglish
Pages (from-to)332-349
Number of pages18
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 2018 Apr 1


  • Conservative discretization
  • Iterative methods
  • Projection method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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