Variational Germano approach for multiscale formulations

I. Akkerman, S.J. Hulshoff, K.G. Zee, van der, R. Borst, de

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    Abstract

    In this chapter the recently introduced Variational Germano procedure is revisited. The procedure is explained using commutativity diagrams. A general Germano identity for all types of discretizations is derived. This relation is similar to the Variational Germano identity, but is not restricted to variational numerical methods. Based on the general Germano identity an alternative algorithm, in the context of stabilized methods, is proposed. This partitioned algorithm consists of distinct building blocks. Several options for these building blocks are presented and analyzed and their performance is tested using a stabilized finite element formulation for the convectionU? diffusion equation. Non-homogenous boundary conditions are shown to pose a serious problem for the dissipation method. This is not the case for the leastsquares method although here the issue of basis dependence occurs. The latter can be circumvented by minimizing a dual-norm of the weak relation instead of the Euclidean norm of the discrete residual.
    Original languageEnglish
    Title of host publicationMultiscale Methods in Computational Mechanics : Progress and Accomplishments
    EditorsR. Borst, de, E. Ramm
    Place of PublicationBerlin
    PublisherSpringer
    Pages53-73
    ISBN (Print)978-90-481-9808-5
    DOIs
    Publication statusPublished - 2011

    Publication series

    NameLecture notes in applied and computational mechanics
    Volume55
    ISSN (Print)1613-7736

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  • Cite this

    Akkerman, I., Hulshoff, S. J., Zee, van der, K. G., & Borst, de, R. (2011). Variational Germano approach for multiscale formulations. In R. Borst, de, & E. Ramm (Eds.), Multiscale Methods in Computational Mechanics : Progress and Accomplishments (pp. 53-73). (Lecture notes in applied and computational mechanics; Vol. 55). Springer. https://doi.org/10.1007/978-90-481-9809-2_4