A low-order nonconforming method for linear elasticity on general meshes

Autor: Daniele Antonio Di Pietro, Alessandra Guglielmana, Michele Botti
Přispěvatelé: Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), ANR-15-CE40-0005,HHOMM,Méthodes hybrides d'ordre élevé sur maillages polyédriques(2015), ANR-17-CE23-0019,Fast4HHO,Solveurs rapides pour des discrétisations robustes en mécanique des fluides(2017)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Polynomial
locking-free methods
Computational Mechanics
General Physics and Astronomy
010103 numerical & computational mathematics
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]
Space (mathematics)
Polyhedral meshes
01 natural sciences
Stability (probability)
Convergence (routing)
Korn's inequality
FOS: Mathematics
Applied mathematics
Polygon mesh
Mathematics - Numerical Analysis
0101 mathematics
Linear elasticity
Mathematics
Hybrid High-Order methods
Degree (graph theory)
65N08
65N30
74B05
74G15
Mechanical Engineering
Numerical Analysis (math.NA)
Computer Science Applications
010101 applied mathematics
Mechanics of Materials
Hybrid high-order methods
Locking-free methods
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering, Elsevier, 2019, 354, pp.96-118. ⟨10.1016/j.cma.2019.05.031⟩
ISSN: 0045-7825
DOI: 10.1016/j.cma.2019.05.031⟩
Popis: In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method, that requires the use of polynomials of degree $k\ge1$ for stability. Specifically, we show that coercivity can be recovered for $k=0$ by introducing a novel term that penalises the jumps of the displacement reconstruction across mesh faces. This term plays a key role in the fulfillment of a discrete Korn inequality on broken polynomial spaces, for which a novel proof valid for general polyhedral meshes is provided. Locking-free error estimates are derived for both the energy- and the $L^2$-norms of the error, that are shown to convergence, for smooth solutions, as $h$ and $h^2$, respectively (here, $h$ denotes the meshsize). A thorough numerical validation on a complete panel of two- and three-dimensional test cases is provided.
Comment: 26 pages, 6 tables, and 4 Figures
Databáze: OpenAIRE
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