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Hybrid high-order methods : a primer with applications to solid mechanics / / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet
| Hybrid high-order methods : a primer with applications to solid mechanics / / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet |
| Autore | Cicuttin Matteo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (138 pages) |
| Disciplina | 531.382 |
| Collana | SpringerBriefs in mathematics |
| Soggetto topico |
Elasticity
Diffusion - Mathematical models Solid state physics Elasticitat Models matemàtics Física de l'estat sòlid |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-81477-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910508430703321 |
Cicuttin Matteo
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hybrid high-order methods : a primer with applications to solid mechanics / / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet
| Hybrid high-order methods : a primer with applications to solid mechanics / / Matteo Cicuttin, Alexandre Ern, Nicolas Pignet |
| Autore | Cicuttin Matteo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (138 pages) |
| Disciplina | 531.382 |
| Collana | SpringerBriefs in mathematics |
| Soggetto topico |
Elasticity
Diffusion - Mathematical models Solid state physics Elasticitat Models matemàtics Física de l'estat sòlid |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-81477-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNISA-996466565403316 |
|
Cicuttin Matteo
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern
| Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern |
| Pubbl/distr/stampa | Beijing, China, : Higher Education Press |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 532.5 |
| Altri autori (Persone) |
WangDeguan
DuquennoiChristian ErnAlexandre <1967-> |
| Collana | Series in contemporary applied mathematics |
| Soggetto topico |
Hydrology - Mathematical models
Physical geography |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-12110-X
9786611121105 981-270-752-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Series Talks; Invited Talks; P. Ackerer, A. Younes: A Finite Volume Formulation of the Mixed Finite Element Method for Triangular Elements; Alexandre Ern: Finite Element Modeling of Hydrosystems with Fully Saturated, Variably Saturated, and Overland Flows; Patrick Goblet: Sharp Front Modeling; Catherine Gourla y, Marie-Helene, Tusseau- Vuillemin: Numerical Modeling of Biological Processes: Specificities, Difficulties and Challenges; Deguan Wang: Ecological Simulation of Red Tides in Shallow Sea Area
Ling Li: Subsurface Pathways of Contaminants to Coastal Waters: Effects of Oceanic OscillationsTingfang Wang, Sixun Huang, Huadong DU, Gui Zhang: Studies on Retrieval of the Initial Values and Diffusion Coefficient of Water Pollutant Advection and Diffusion Process; Jing Chen, Zhifang Zhou: Application of Tabu Search Method to the Parameters of Groundwater Simulation Models; Xiaomin Xu, Deguan Wang: Several Problems in River Networks Hydraulic Mathematics Model Jue Yang, Deguan Wang, Ying Zhang: Study on the Character of Equilibrium Point and Its Impact on the Changing Rate of Phytoplankton Concentration Using a Simple Nutrient-Phytoplankton ModelJie Zhou, Deguan Wang, Haiping Jiang, Xijun Lai: A Numerical Simulation of Thermal Discharge into Tidal Estuary with FVM |
| Record Nr. | UNINA-9910450704903321 |
| Beijing, China, : Higher Education Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern
| Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern |
| Pubbl/distr/stampa | Beijing, China, : Higher Education Press |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 532.5 |
| Altri autori (Persone) |
WangDeguan
DuquennoiChristian ErnAlexandre <1967-> |
| Collana | Series in contemporary applied mathematics |
| Soggetto topico |
Hydrology - Mathematical models
Physical geography |
| ISBN |
1-281-12110-X
9786611121105 981-270-752-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Series Talks; Invited Talks; P. Ackerer, A. Younes: A Finite Volume Formulation of the Mixed Finite Element Method for Triangular Elements; Alexandre Ern: Finite Element Modeling of Hydrosystems with Fully Saturated, Variably Saturated, and Overland Flows; Patrick Goblet: Sharp Front Modeling; Catherine Gourla y, Marie-Helene, Tusseau- Vuillemin: Numerical Modeling of Biological Processes: Specificities, Difficulties and Challenges; Deguan Wang: Ecological Simulation of Red Tides in Shallow Sea Area
Ling Li: Subsurface Pathways of Contaminants to Coastal Waters: Effects of Oceanic OscillationsTingfang Wang, Sixun Huang, Huadong DU, Gui Zhang: Studies on Retrieval of the Initial Values and Diffusion Coefficient of Water Pollutant Advection and Diffusion Process; Jing Chen, Zhifang Zhou: Application of Tabu Search Method to the Parameters of Groundwater Simulation Models; Xiaomin Xu, Deguan Wang: Several Problems in River Networks Hydraulic Mathematics Model Jue Yang, Deguan Wang, Ying Zhang: Study on the Character of Equilibrium Point and Its Impact on the Changing Rate of Phytoplankton Concentration Using a Simple Nutrient-Phytoplankton ModelJie Zhou, Deguan Wang, Haiping Jiang, Xijun Lai: A Numerical Simulation of Thermal Discharge into Tidal Estuary with FVM |
| Record Nr. | UNINA-9910784038703321 |
| Beijing, China, : Higher Education Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern
| Mathematical methods for surface and subsurface hydrosystems [[electronic resource] /] / editors, Deguan Wang, Christian Duquennoi, Alexandre Ern |
| Pubbl/distr/stampa | Beijing, China, : Higher Education Press |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 532.5 |
| Altri autori (Persone) |
WangDeguan
DuquennoiChristian ErnAlexandre <1967-> |
| Collana | Series in contemporary applied mathematics |
| Soggetto topico |
Hydrology - Mathematical models
Physical geography |
| ISBN |
1-281-12110-X
9786611121105 981-270-752-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Series Talks; Invited Talks; P. Ackerer, A. Younes: A Finite Volume Formulation of the Mixed Finite Element Method for Triangular Elements; Alexandre Ern: Finite Element Modeling of Hydrosystems with Fully Saturated, Variably Saturated, and Overland Flows; Patrick Goblet: Sharp Front Modeling; Catherine Gourla y, Marie-Helene, Tusseau- Vuillemin: Numerical Modeling of Biological Processes: Specificities, Difficulties and Challenges; Deguan Wang: Ecological Simulation of Red Tides in Shallow Sea Area
Ling Li: Subsurface Pathways of Contaminants to Coastal Waters: Effects of Oceanic OscillationsTingfang Wang, Sixun Huang, Huadong DU, Gui Zhang: Studies on Retrieval of the Initial Values and Diffusion Coefficient of Water Pollutant Advection and Diffusion Process; Jing Chen, Zhifang Zhou: Application of Tabu Search Method to the Parameters of Groundwater Simulation Models; Xiaomin Xu, Deguan Wang: Several Problems in River Networks Hydraulic Mathematics Model Jue Yang, Deguan Wang, Ying Zhang: Study on the Character of Equilibrium Point and Its Impact on the Changing Rate of Phytoplankton Concentration Using a Simple Nutrient-Phytoplankton ModelJie Zhou, Deguan Wang, Haiping Jiang, Xijun Lai: A Numerical Simulation of Thermal Discharge into Tidal Estuary with FVM |
| Record Nr. | UNINA-9910823063203321 |
| Beijing, China, : Higher Education Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||