Academic Journal
Finite element approximation of a strain-limiting elastic model
| العنوان: | Finite element approximation of a strain-limiting elastic model |
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| المؤلفون: | Bonito, Andrea, Girault, Vivette, Süli, Endre |
| المساهمون: | Department of Mathematics Texas (TAMU), Texas A&M University College Station, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University of Oxford |
| المصدر: | ISSN: 0272-4979. |
| بيانات النشر: | HAL CCSD Oxford University Press (OUP) |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | strain-limiting elastic model finite element method convergence decoupled iterative method, [MATH]Mathematics [math] |
| الوصف: | International audience ; We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in R d , d ∈ {2, 3}. The sequence of finite element approximations is shown to exhibit strong convergence to the unique weak solution of the model. A rate of convergence for the sequence of finite element approximations is shown provided that the material parameters featuring in the model are Lipschitz continuous and that the exact solution possesses additional regularity. A rate of convergence for the sequence of finite element approximations is shown provided that the material parameters featuring in the model are Lipschitz continuous and that the exact solution possesses additional regularity. An iterative algorithm is constructed for the solution of the system of nonlinear algebraic equations that arises from the finite element approximation. An appealing feature of the iterative algorithm is that it decouples the monotone and linear elastic parts of the nonlinearity in the model. In particular, our choice of piecewise constant approximation for the stress tensor (and continuous piecewise linear approximation for the displacement) allows us to compute the monotone part of the nonlinearity by solving an algebraic system with d(d + 1)/2 unknowns independently on each element in the subdivision of the computational domain. The theoretical results are illustrated by numerical experiments. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-03876297; https://hal.science/hal-03876297; https://hal.science/hal-03876297/document; https://hal.science/hal-03876297/file/Bonito.G.Suli.HAL.pdf |
| DOI: | 10.1093/imanum/dry065 |
| الاتاحة: | https://hal.science/hal-03876297 https://hal.science/hal-03876297/document https://hal.science/hal-03876297/file/Bonito.G.Suli.HAL.pdf https://doi.org/10.1093/imanum/dry065 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.4882A623 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1093/imanum/dry065 |
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