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

Andrea Bonito, Irene Kyza, Ricardo H. Nochetto

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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. © 2013 Springer-Verlag Berlin Heidelberg.
Original languageEnglish (US)
Pages (from-to)225-257
Number of pages33
JournalNumerische Mathematik
Volume125
Issue number2
DOIs
StatePublished - Mar 16 2013
Externally publishedYes

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