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Time-discrete higher order ALE formulations: a priori error analysis |
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| Authors: | Andrea Bonito Irene Kyza Ricardo H Nochetto |
| Institution: | 1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA 2. Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13, Heraklion-Crete, Greece 3. Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD, 20742-4015, USA |
| 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. |
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