A multiscale/stabilized finite element method for the advection-diffusion equation

A. Masud*, Rooh Ul Amin Khurram

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    113 Scopus citations


    This paper presents a multiscale method that yields a stabilized finite element formulation for the advection-diffusion equation. The multiscale method arises from a decomposition of the scalar field into coarse (resolved) scale and fine (unresolved) scale. The resulting stabilized formulation possesses superior properties like that of the SUPG and the GLS methods. A significant feature of the present method is that the definition of the stabilization term appears naturally, and therefore the formulation is free of any user-designed or user-defined parameters. Another important ingredient is that since the method is residual based, it satisfies consistency ab initio. Based on the proposed formulation, a family of 2-D elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed. Numerical results show the good performance of the method on uniform, skewed as well as composite meshes and confirm convergence at optimal rates.

    Original languageEnglish (US)
    Pages (from-to)1997-2018
    Number of pages22
    JournalComputer Methods in Applied Mechanics and Engineering
    Issue number21-22
    StatePublished - May 28 2004

    ASJC Scopus subject areas

    • Computational Mechanics
    • Mechanics of Materials
    • Mechanical Engineering
    • Physics and Astronomy(all)
    • Computer Science Applications


    Dive into the research topics of 'A multiscale/stabilized finite element method for the advection-diffusion equation'. Together they form a unique fingerprint.

    Cite this