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Mixed finite element methods and applications / / Daniele Boffi, Franco Brezzi, Michel Fortin
| Mixed finite element methods and applications / / Daniele Boffi, Franco Brezzi, Michel Fortin |
| Autore | Boffi Daniele |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (xiv, 685 pages) : illustrations |
| Disciplina | 518.25 |
| Altri autori (Persone) |
BrezziF <1945-> (Franco)
FortinMichel |
| Collana | Springer series in computational mathematics |
| Soggetto topico | Finite element method |
| ISBN | 3-642-36519-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Variational Formulations and Finite Element Methods -- Function Spaces and Finite Element Approximations -- Algebraic Aspects of Saddle Point Problems -- Saddle Point Problems in Hilbert spaces -- Approximation of Saddle Point Problems -- Complements: Stabilisation Methods, Eigenvalue Problems -- Mixed Methods for Elliptic Problems -- Incompressible Materials and Flow Problems -- Complements on Elasticity Problems -- Complements on Plate Problems -- Mixed Finite Elements for Electromagnetic Problems -- Index. . |
| Record Nr. | UNINA-9910437872003321 |
Boffi Daniele
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| New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mixed Finite Elements, Compatibility Conditions, and Applications [[electronic resource] ] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006 / / by Daniele Boffi, Franco Brezzi, Leszek F. Demkowicz, Ricardo G. Durán, Richard S. Falk, Michel Fortin ; edited by Daniele Boffi, Lucia Gastaldi
| Mixed Finite Elements, Compatibility Conditions, and Applications [[electronic resource] ] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006 / / by Daniele Boffi, Franco Brezzi, Leszek F. Demkowicz, Ricardo G. Durán, Richard S. Falk, Michel Fortin ; edited by Daniele Boffi, Lucia Gastaldi |
| Autore | Boffi Daniele |
| Edizione | [1st ed. 2008.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008 |
| Descrizione fisica | 1 online resource (X, 244 p. 36 illus.) |
| Disciplina | 620.00151535 |
| Collana | C.I.M.E. Foundation Subseries |
| Soggetto topico |
Numerical analysis
Partial differential equations Physics Continuum physics Global analysis (Mathematics) Manifolds (Mathematics) Numerical Analysis Partial Differential Equations Numerical and Computational Physics, Simulation Classical and Continuum Physics Global Analysis and Analysis on Manifolds |
| ISBN | 3-540-78319-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Mixed Finite Element Methods -- Finite Elements for the Stokes Problem -- Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations -- Finite Element Methods for Linear Elasticity -- Finite Elements for the Reissner–Mindlin Plate. |
| Record Nr. | UNISA-996466537103316 |
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Boffi Daniele
|
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| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Mixed Finite Elements, Compatibility Conditions, and Applications : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006 / / by Daniele Boffi, Franco Brezzi, Leszek F. Demkowicz, Ricardo G. Durán, Richard S. Falk, Michel Fortin ; edited by Daniele Boffi, Lucia Gastaldi
| Mixed Finite Elements, Compatibility Conditions, and Applications : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006 / / by Daniele Boffi, Franco Brezzi, Leszek F. Demkowicz, Ricardo G. Durán, Richard S. Falk, Michel Fortin ; edited by Daniele Boffi, Lucia Gastaldi |
| Autore | Boffi Daniele |
| Edizione | [1st ed. 2008.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008 |
| Descrizione fisica | 1 online resource (X, 244 p. 36 illus.) |
| Disciplina | 620.00151535 |
| Collana | C.I.M.E. Foundation Subseries |
| Soggetto topico |
Numerical analysis
Differential equations, Partial Physics Field theory (Physics) Global analysis (Mathematics) Manifolds (Mathematics) Numerical Analysis Partial Differential Equations Numerical and Computational Physics, Simulation Classical and Continuum Physics Global Analysis and Analysis on Manifolds |
| ISBN | 3-540-78319-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Mixed Finite Element Methods -- Finite Elements for the Stokes Problem -- Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations -- Finite Element Methods for Linear Elasticity -- Finite Elements for the Reissner–Mindlin Plate. |
| Record Nr. | UNINA-9910483123003321 |
|
Boffi Daniele
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems / / Jean Deteix, Thierno Diop and Michel Fortin
| Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems / / Jean Deteix, Thierno Diop and Michel Fortin |
| Autore | Deteix Jean |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (119 pages) |
| Disciplina | 620.00151535 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Finite element method
Mètode dels elements finits |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-12616-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 2 Mixed Problems -- 2.1 Some Reminders About Mixed Problems -- 2.1.1 The Saddle Point Formulation -- 2.1.2 Existence of a Solution -- 2.1.3 Dual Problem -- 2.1.4 A More General Case: A Regular Perturbation -- 2.1.5 The Case -- 2.2 The Discrete Problem -- 2.2.1 Error Estimates -- 2.2.2 The Matricial Form of the Discrete Problem -- 2.2.3 The Discrete Dual Problem: The Schur Complement -- 2.3 Augmented Lagrangian -- 2.3.1 Augmented or Regularised Lagrangians -- 2.3.2 Discrete Augmented Lagrangian in Matrix Form -- 2.3.3 Augmented Lagrangian and the Condition Number of the Dual Problem -- 2.3.4 Augmented Lagrangian: An Iterated Penalty -- 3 Iterative Solvers for Mixed Problems -- 3.1 Classical Iterative Methods -- 3.1.1 Some General Points -- Linear Algebra and Optimisation -- Norms -- Krylov Subspace -- Preconditioning -- 3.1.2 The Preconditioned Conjugate Gradient Method -- 3.1.3 Constrained Problems: Projected Gradient and Variants -- Equality Constraints: The Projected Gradient Method -- Inequality Constraints -- Positivity Constraints -- Convex Constraints -- 3.1.4 Hierarchical Basis and Multigrid Preconditioning -- 3.1.5 Conjugate Residuals, Minres, Gmres and the Generalised Conjugate Residual Algorithm -- The Generalised Conjugate Residual Method -- The Left Preconditioning -- The Right Preconditioning -- The Gram-Schmidt Algorithm -- GCR for Mixed Problems -- 3.2 Preconditioners for the Mixed Problem -- 3.2.1 Factorisation of the System -- Solving Using the Factorisation -- 3.2.2 Approximate Solvers for the Schur Complement and the Uzawa Algorithm -- The Uzawa Algorithm -- 3.2.3 The General Preconditioned Algorithm -- 3.2.4 Augmented Lagrangian as a Perturbed Problem -- 4 Numerical Results: Cases Where Q= Q -- 4.1 Mixed Laplacian Problem -- 4.1.1 Formulation of the Problem.
4.1.2 Discrete Problem and Classic Numerical Methods -- The Augmented Lagrangian Formulation -- 4.1.3 A Numerical Example -- 4.2 Application to Incompressible Elasticity -- 4.2.1 Nearly Incompressible Linear Elasticity -- 4.2.2 Neo-Hookean and Mooney-Rivlin Materials -- Mixed Formulation for Mooney-Rivlin Materials -- 4.2.3 Numerical Results for the Linear Elasticity Problem -- 4.2.4 The Mixed-GMP-GCR Method -- Approximate Solver in u -- 4.2.5 The Test Case -- Number of Iterations and Mesh Size -- Comparison of the Preconditioners of Sect.3.2 -- Effect of the Solver in u -- 4.2.6 Large Deformation Problems -- Neo-Hookean Material -- Mooney-Rivlin Material -- 4.3 Navier-Stokes Equations -- 4.3.1 A Direct Iteration: Regularising the Problem -- 4.3.2 A Toy Problem -- 5 Contact Problems: A Case Where Q≠Q -- 5.1 Imposing Dirichlet's Condition Through a Multiplier -- 5.1.1 and Its Dual -- 5.1.2 A Steklov-Poincaré operator -- Using This as a Solver -- 5.1.3 Discrete Problems -- The Matrix Form and the Discrete Schur Complement -- 5.1.4 A Discrete Steklov-Poincaré Operator -- 5.1.5 Computational Issues, Approximate Scalar Product -- Simplified Forms of the ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S script upper P Subscript h) /StPNE pdfmark [/StBMC pdfmarkSPhps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Operator and Preconditioning -- 5.1.6 The Formulation -- The Choice of h -- 5.1.7 A Toy Model for the Contact Problem -- The Discrete Formulation -- The Active Set Strategy -- 5.2 Sliding Contact -- 5.2.1 The Discrete Contact Problem -- Contact Status -- 5.2.2 The Algorithm for Sliding Contact -- A Newton Method -- The Active Set Strategy -- 5.2.3 A Numerical Example of Contact Problem -- 6 Solving Problems with More Than One Constraint -- 6.1 A Model Problem -- 6.2 Interlaced Method -- 6.3 Preconditioners Based on Factorisation. 6.3.1 The Sequential Method -- 6.4 An Alternating Procedure -- 7 Conclusion -- Bibliography -- Index. |
| Record Nr. | UNINA-9910595041303321 |
|
Deteix Jean
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems / / Jean Deteix, Thierno Diop and Michel Fortin
| Numerical methods for mixed finite element problems : applications to incompressible materials and contact problems / / Jean Deteix, Thierno Diop and Michel Fortin |
| Autore | Deteix Jean |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (119 pages) |
| Disciplina | 620.00151535 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Finite element method
Mètode dels elements finits |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-12616-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 2 Mixed Problems -- 2.1 Some Reminders About Mixed Problems -- 2.1.1 The Saddle Point Formulation -- 2.1.2 Existence of a Solution -- 2.1.3 Dual Problem -- 2.1.4 A More General Case: A Regular Perturbation -- 2.1.5 The Case -- 2.2 The Discrete Problem -- 2.2.1 Error Estimates -- 2.2.2 The Matricial Form of the Discrete Problem -- 2.2.3 The Discrete Dual Problem: The Schur Complement -- 2.3 Augmented Lagrangian -- 2.3.1 Augmented or Regularised Lagrangians -- 2.3.2 Discrete Augmented Lagrangian in Matrix Form -- 2.3.3 Augmented Lagrangian and the Condition Number of the Dual Problem -- 2.3.4 Augmented Lagrangian: An Iterated Penalty -- 3 Iterative Solvers for Mixed Problems -- 3.1 Classical Iterative Methods -- 3.1.1 Some General Points -- Linear Algebra and Optimisation -- Norms -- Krylov Subspace -- Preconditioning -- 3.1.2 The Preconditioned Conjugate Gradient Method -- 3.1.3 Constrained Problems: Projected Gradient and Variants -- Equality Constraints: The Projected Gradient Method -- Inequality Constraints -- Positivity Constraints -- Convex Constraints -- 3.1.4 Hierarchical Basis and Multigrid Preconditioning -- 3.1.5 Conjugate Residuals, Minres, Gmres and the Generalised Conjugate Residual Algorithm -- The Generalised Conjugate Residual Method -- The Left Preconditioning -- The Right Preconditioning -- The Gram-Schmidt Algorithm -- GCR for Mixed Problems -- 3.2 Preconditioners for the Mixed Problem -- 3.2.1 Factorisation of the System -- Solving Using the Factorisation -- 3.2.2 Approximate Solvers for the Schur Complement and the Uzawa Algorithm -- The Uzawa Algorithm -- 3.2.3 The General Preconditioned Algorithm -- 3.2.4 Augmented Lagrangian as a Perturbed Problem -- 4 Numerical Results: Cases Where Q= Q -- 4.1 Mixed Laplacian Problem -- 4.1.1 Formulation of the Problem.
4.1.2 Discrete Problem and Classic Numerical Methods -- The Augmented Lagrangian Formulation -- 4.1.3 A Numerical Example -- 4.2 Application to Incompressible Elasticity -- 4.2.1 Nearly Incompressible Linear Elasticity -- 4.2.2 Neo-Hookean and Mooney-Rivlin Materials -- Mixed Formulation for Mooney-Rivlin Materials -- 4.2.3 Numerical Results for the Linear Elasticity Problem -- 4.2.4 The Mixed-GMP-GCR Method -- Approximate Solver in u -- 4.2.5 The Test Case -- Number of Iterations and Mesh Size -- Comparison of the Preconditioners of Sect.3.2 -- Effect of the Solver in u -- 4.2.6 Large Deformation Problems -- Neo-Hookean Material -- Mooney-Rivlin Material -- 4.3 Navier-Stokes Equations -- 4.3.1 A Direct Iteration: Regularising the Problem -- 4.3.2 A Toy Problem -- 5 Contact Problems: A Case Where Q≠Q -- 5.1 Imposing Dirichlet's Condition Through a Multiplier -- 5.1.1 and Its Dual -- 5.1.2 A Steklov-Poincaré operator -- Using This as a Solver -- 5.1.3 Discrete Problems -- The Matrix Form and the Discrete Schur Complement -- 5.1.4 A Discrete Steklov-Poincaré Operator -- 5.1.5 Computational Issues, Approximate Scalar Product -- Simplified Forms of the ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S script upper P Subscript h) /StPNE pdfmark [/StBMC pdfmarkSPhps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Operator and Preconditioning -- 5.1.6 The Formulation -- The Choice of h -- 5.1.7 A Toy Model for the Contact Problem -- The Discrete Formulation -- The Active Set Strategy -- 5.2 Sliding Contact -- 5.2.1 The Discrete Contact Problem -- Contact Status -- 5.2.2 The Algorithm for Sliding Contact -- A Newton Method -- The Active Set Strategy -- 5.2.3 A Numerical Example of Contact Problem -- 6 Solving Problems with More Than One Constraint -- 6.1 A Model Problem -- 6.2 Interlaced Method -- 6.3 Preconditioners Based on Factorisation. 6.3.1 The Sequential Method -- 6.4 An Alternating Procedure -- 7 Conclusion -- Bibliography -- Index. |
| Record Nr. | UNISA-996490271503316 |
|
Deteix Jean
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||