Time-discrete higher order ALE formulations: a priori error analysis
KAUST Grant NumberKUS-C1-016-04
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AbstractWe 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.
CitationBonito A, Kyza I, Nochetto RH (2013) Time-discrete higher order ALE formulations: a priori error analysis. Numerische Mathematik 125: 225–257. Available: http://dx.doi.org/10.1007/s00211-013-0539-3.
SponsorsA.B. was partially supported by NSF Grant DMS-0914977 and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). I.K. was partially supported by the European Social Fund (ESF)-European Union (EU) and National Resources of the Greek State within the framework of the Action "Supporting Postdoctoral Researchers" of the Operational Programme "Education and Lifelong Learning (EdLL)" and by NSF Grants DMS-0807811 and DMS-0807815. R.H.N. was partially supported by NSF Grants DMS-0807811 and DMS-1109325.