Time-integration schemes for the finite element dynamic Signorini problem
| Autor: | David Doyen, Serge Piperno, Alexandre Ern |
|---|---|
| Přispěvatelé: | EDF (EDF), Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
time-integration schemes
Class (set theory) Mathematical optimization Applied Mathematics modified mass method Mass matrix Finite element method elastodynamics frictionless unilateral contact Computational Mathematics Benchmark (computing) 65M20 65M60 74H15 74M15 74S05 finite elements Contact condition Variety (universal algebra) Signorini problem Enforcement [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing SIAM Journal on Scientific Computing, 2011, 33 (1), pp.223-249. ⟨10.1137/100791440⟩ |
| ISSN: | 1064-8275 |
| DOI: | 10.1137/100791440⟩ |
| Popis: | International audience; The discretization of the dynamic Signorini problem with finite elements in space and a time-stepping scheme is not straightforward. Consequently a large variety of methods for this problem have been designed over the last two decades. Up to date, no systematic comparison of such methods has been performed. The aim of the present work is to classify and compare them. For each method, we discuss the presence of spurious oscillations and the energy conservation. For explicit approaches, the stability condition on the time step is also discussed. Numerical simulations on two 1D benchmark problems with analytical solutions illustrate the properties of the different methods. Most of the discretizations considered herein can be found in the literature, but the semi-explicit modified mass method is new and features, in our opinion, several attractive properties. |
| Databáze: | OpenAIRE |
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