Hybrid high-order methods : a primer with applications to solid mechanics / / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet

• Autore: Cicuttin Matteo
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (138 pages)
• Disciplina: 531.382
• Soggetto topico: Elasticity; Diffusion - Mathematical models; Solid state physics; Elasticitat; Models matemàtics; Física de l'estat sòlid
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): ErnAlexandre <1967->; PignetNicolas
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Getting Started: Linear Diffusion -- 1.1 Model Problem -- 1.2 Discrete Setting -- 1.2.1 The Mesh -- 1.2.2 Discrete Unknowns -- 1.3 Local Reconstruction and Stabilization -- 1.3.1 Local Reconstruction -- 1.3.2 Local Stabilization -- 1.3.3 Example: Lowest-Order Case -- 1.4 Assembly and Static Condensation -- 1.4.1 The Discrete Problem -- 1.4.2 Algebraic Realization -- 1.5 Flux Recovery and Embedding into HDG Methods -- 1.5.1 Flux Recovery -- 1.5.2 Embedding into HDG Methods -- 1.6 One-Dimensional Setting -- 2 Mathematical Aspects -- 2.1 Mesh Regularity and Basic Analysis Tools -- 2.1.1 Mesh Regularity -- 2.1.2 Functional and Discrete Inverse Inequalities -- 2.1.3 Polynomial Approximation -- 2.2 Stability -- 2.3 Consistency -- 2.4 H1-Error Estimate -- 2.5 Improved L2-Error Estimate -- 3 Some Variants -- 3.1 Variants on Gradient Reconstruction -- 3.2 Mixed-Order Variant and Application to Curved Boundaries -- 3.2.1 Mixed-Order Variant with Higher Cell Degree -- 3.2.2 Domains with a Curved Boundary -- 3.3 Finite Element and Virtual Element Viewpoints -- 4 Linear Elasticity and Hyperelasticity -- 4.1 Continuum Mechanics -- 4.1.1 Infinitesimal Deformations and Linear Elasticity -- 4.1.2 Finite Deformations and Hyperelasticity -- 4.2 HHO Methods for Linear Elasticity -- 4.2.1 Discrete Unknowns, Reconstruction, and Stabilization -- 4.2.2 Discrete Problem, Energy Minimization, and Traction Recovery -- 4.2.3 Stability and Error Analysis -- 4.3 HHO Methods for Hyperelasticity -- 4.3.1 The Stabilized HHO Method -- 4.3.2 The Unstabilized HHO Method -- 4.3.3 Nonlinear Solver and Static Condensation -- 4.4 Numerical Examples -- 5 Elastodynamics -- 5.1 Second-Order Formulation in Time -- 5.1.1 HHO Space Semi-discretization -- 5.1.2 Time Discretization -- 5.2 First-Order Formulation in Time -- 5.2.1 HHO Space Semi-discretization. ; 5.2.2 Time Discretization -- 5.3 Numerical Example -- 6 Contact and Friction -- 6.1 Model Problem -- 6.2 HHO-Nitsche Method -- 6.2.1 FEM-Nitsche Method -- 6.2.2 Discrete Setting for HHO-Nitsche -- 6.2.3 Stability and Error Analysis -- 6.3 Numerical Example -- 7 Plasticity -- 7.1 Plasticity Model -- 7.1.1 Kinematics and Additive Decomposition -- 7.1.2 Helmholtz Free Energy and Yield Function -- 7.1.3 Plasticity Problem in Incremental Form -- 7.2 HHO Discretizations -- 7.2.1 Discrete Unknowns -- 7.2.2 Discrete Plasticity Problem in Incremental Form -- 7.2.3 Nonlinear Solver -- 7.3 Numerical Examples -- 7.3.1 Torsion of a Square-Section Bar -- 7.3.2 Hydraulic Pump Under Internal Forces -- 8 Implementation Aspects -- 8.1 Polynomial Spaces -- 8.2 Algebraic Representation of the HHO Space -- 8.3 L2-Orthogonal Projections -- 8.3.1 Quadratures -- 8.3.2 Reduction Operator -- 8.4 Algebraic Realization of the Local HHO Operators -- 8.4.1 Local Reconstruction Operator -- 8.4.2 The Stabilization Operator -- 8.5 Assembly and Boundary Conditions -- 8.6 Remarks on the Computational Cost of HHO Methods -- Appendix References.
• Titolo autorizzato: Hybrid high-order methods
• ISBN: 3-030-81477-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910508430703321
• Lo trovi qui: Univ. Federico II
• Serie: SpringerBriefs in mathematics.