A DG approach to higher order ALE formulations in time

Andrea Bonito, Irene Kyza, Ricardo H. Nochetto

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    Abstract

    We review recent results [10, 9, 8] on time-discrete discontinuous Ga- lerkin (dG) methods for advection-diffusion model problems defined on deformable do- mains and written on the Arbitrary Lagrangian Eulerian (ALE) framework. ALE for- mulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. We describe the construction of higher order in time numerical schemes enjoying stability properties independent of the arbitrary extension chosen. Our approach is based on the validity of Reynolds’ identity for dG methods which generalize to higher order schemes the Geometric Conservation Law (GCL) condition. Stability, a priori and a posteriori error analyses are briefly discussed and illustrated by insightful numerical experiments.
    Original languageEnglish
    Title of host publicationRecent developments in discontinuous Galerkin finite element methods for partial differential equations
    EditorsXiaobing Feng, Ohannes Karakashian , Yulong Xing
    PublisherSpringer International Publishing
    Pages223-258
    Number of pages36
    ISBN (Electronic)9783319018188
    ISBN (Print)9783319018171
    DOIs
    Publication statusPublished - 2014

    Publication series

    NameIMA volumes in mathematics and its applications
    PublisherSpringer International
    Volume157

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    Cite this

    Bonito, A., Kyza, I., & Nochetto, R. H. (2014). A DG approach to higher order ALE formulations in time. In X. Feng, O. Karakashian , & Y. Xing (Eds.), Recent developments in discontinuous Galerkin finite element methods for partial differential equations (pp. 223-258). (IMA volumes in mathematics and its applications; Vol. 157). Springer International Publishing. https://doi.org/10.1007/978-3-319-01818-8_10