Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis
| Autor: | Rita Riedlbeck, Sylvie Granet, Daniele Antonio Di Pietro, Alexandre Ern, Kyrylo Kazymyrenko |
|---|---|
| Přispěvatelé: | 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)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-15-CE40-0005,HHOMM,Méthodes hybrides d'ordre élevé sur maillages polyédriques(2015) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Spacetime
Cauchy stress tensor Mathematical analysis Estimator Flux Geometry 010103 numerical & computational mathematics 01 natural sciences Finite element method Mathematics::Numerical Analysis 010101 applied mathematics Stress (mechanics) Computational Mathematics Test case Computational Theory and Mathematics Arnold-Winther finite element space Modeling and Simulation A priori and a posteriori equilibrated stress reconstruction 0101 mathematics a posteriori error estimate Biot's poro-elasticity problem [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | Computers & Mathematics with Applications Computers & Mathematics with Applications, 2017, 73 (7), pp.1593-1610. ⟨10.1016/j.camwa.2017.02.005⟩ Computers & Mathematics with Applications, Elsevier, 2017, 73 (7), pp.1593-1610. ⟨10.1016/j.camwa.2017.02.005⟩ |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2017.02.005⟩ |
| Popis: | International audience; We derive equilibrated reconstructions of the Darcy velocity and of the total stress ten-sor for Biot's poro-elasticity problem. Both reconstructions are obtained from mixed finite element solutions of local Neumann problems posed over patches of elements around mesh vertices. The Darcy velocity is reconstructed using Raviart–Thomas finite elements and the stress tensor using Arnold–Winther finite elements so that the reconstructed stress tensor is symmetric. Both reconstructions have continuous normal component across mesh interfaces. Using these reconstructions, we derive a posteriori error estimators for Biot's poro-elasticity problem, and we devise an adaptive space-time algorithm driven by these estimators. The algorithm is illustrated on test cases with analytical solution, on the quarter five-spot problem , and on an industrial test case simulating the excavation of two galleries. |
| Databáze: | OpenAIRE |
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