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

Andrea Bonito; Irene Kyza; Ricardo H. Nochetto

doi:10.1007/s00211-013-0539-3

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

Andrea Bonito, Irene Kyza, Ricardo H. Nochetto

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12 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 language	English (US)
Pages (from-to)	225-257
Number of pages	33
Journal	Numerische Mathematik
Volume	125
Issue number	2
DOIs	https://doi.org/10.1007/s00211-013-0539-3
State	Published - Mar 16 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: A.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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "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. {\textcopyright} 2013 Springer-Verlag Berlin Heidelberg.",

author = "Andrea Bonito and Irene Kyza and Nochetto, {Ricardo H.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: A.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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Kyza, Irene

AU - Nochetto, Ricardo H.

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PY - 2013/3/16

Y1 - 2013/3/16

N2 - 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.

AB - 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.

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DO - 10.1007/s00211-013-0539-3

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SP - 225

EP - 257

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 2

ER -

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

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