Time-discrete higher order ALE formulations: A priori error analysis

Andrea Bonito, Irene Kyza (Lead / Corresponding author), Ricardo H. Nochetto

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results.

    Original languageEnglish
    Pages (from-to)225-257
    Number of pages33
    JournalNumerische Mathematik
    Volume125
    Issue number2
    DOIs
    Publication statusPublished - Oct 2013

    Fingerprint

    Dive into the research topics of 'Time-discrete higher order ALE formulations: A priori error analysis'. Together they form a unique fingerprint.

    Cite this