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

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.

authors

• Bonito, Andrea

published proceedings

• NUMERISCHE MATHEMATIK

author list (cited authors)

• Bonito, A., Kyza, I., & Nochetto, R. H.

citation count

• 12

complete list of authors

• Bonito, Andrea||Kyza, Irene||Nochetto, Ricardo H

publication date

• October 2013

publisher

• Springer Nature  Publisher

published in

• Numerische Mathematik  Journal

keywords

• 49 Mathematical Sciences
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00211-013-0539-3

start page

• 225

end page

• 257

volume

• 125

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00211-013-0539-3