A stabilized mixed finite element method for the first-order form of advection-diffusion equation

Arif Masud, Jae Hyuk Kwack

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a stabilized mixed finite element method for the first-order form of advection-diffusion equation. The new method is based on an additive split of the flux-field into coarse- and fine-scale components that systematically lead to coarse and fine-scale variational formulations. Solution of the fine-scale variational problem is mathematically embedded in the coarse-scale problem and this yields the resulting method. A key feature of the method is that the characteristic length scale of the mesh does not appear explicitly in the definition of the stability parameter that emerges via the solution of the fine-scale problem. The new method yields a family of equal- and unequal-order elements that show stable response on structured and unstructured meshes for a variety of benchmark problems.

Original languageEnglish (US)
Pages (from-to)1321-1348
Number of pages28
JournalInternational Journal for Numerical Methods in Fluids
Volume57
Issue number9
DOIs
StatePublished - Jul 30 2008

Keywords

  • Advection-diffusion equation
  • Continuous fields of arbitrary order
  • Equal- and unequal-order elements
  • Multiscale methods
  • Stabilized methods

ASJC Scopus subject areas

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

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