Equilibrated stress tensor reconstruction and a posteriori error estimation for nonlinear elasticity
| Autor: | Rita Riedlbeck, Michele Botti |
|---|---|
| Přispěvatelé: | Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Adaptive algorithm Discretization Cauchy stress tensor Applied Mathematics A Posteriori Error Estimate Linear elasticity Numerical Analysis (math.NA) 010103 numerical & computational mathematics Equilibrated Stress Reconstruction 01 natural sciences 010101 applied mathematics Stress (mechanics) Computational Mathematics Arnold-Falk-Winther Finite Element Linearization Hyperelastic material FOS: Mathematics Applied mathematics A priori and a posteriori Nonlinear Elasticity Mathematics - Numerical Analysis 0101 mathematics [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | Computational Methods in Applied Mathematics Computational Methods in Applied Mathematics, De Gruyter, 2018, ⟨10.1515/cmam-2018-0012⟩ Computational Methods in Applied Mathematics, 2018, ⟨10.1515/cmam-2018-0012⟩ |
| ISSN: | 2018-0012 1609-4840 |
| DOI: | 10.1515/cmam-2018-0012⟩ |
| Popis: | We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, H ( div ) {H(\mathrm{div)}} -conforming stress tensor reconstructions, obtained from local problems on patches around vertices using the Arnold–Falk–Winther finite element spaces. We distinguish two stress reconstructions: one for the discrete stress and one representing the linearization error. The reconstructions are independent of the mechanical behavior law. Based on these stress tensor reconstructions, we derive an a posteriori error estimate distinguishing the discretization, linearization, and quadrature error estimates, and propose an adaptive algorithm balancing these different error sources. We prove the efficiency of the estimate, and confirm it on a numerical test with an analytical solution. We then apply the adaptive algorithm to a more application-oriented test, considering the Hencky–Mises and an isotropic damage model. |
| Databáze: | OpenAIRE |
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