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 Quarteroni, Alfio, author.
 Third edition.  Cham, Switzerland : Springer, [2017]
 Description
 Book — xvii, 681 pages : illustrations (some color) ; 25 cm.
 Summary

 1 A brief survey of partial differential equations. 2 Elements of functional analysis. 3 Elliptic equations. 4 The Galerkin finite element method for elliptic problems. 5 Parabolic equations. 6 Generation of 1D and 2D grids. 7 Algorithms for the solution of linear systems. 8 Elements of finite element programming. 9 The finite volume method. 10 Spectral methods. 11 Isogeometric analysis. 12 Discontinuous element methods (D Gandmortar). 13 Diffusiontransportreaction equations. 14 Finite differences for hyperbolic equations. 15 Finite elements and spectral methods for hyperbolic equations. 16 Nonlinear hyperbolic problems. 17 NavierStokes equations. 18 Optimal control of partial differential equations. 19 Domain decomposition methods. 20 Reduced basis approximation for parametrized partial differential equations. References.
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QA377 .Q375 2017  Unknown 
 Modellistica numerica per problemi differenziali. English
 Quarteroni, Alfio.
 Milan ; New York : Springer, ©2009.
 Description
 Book — 1 online resource (xvi, 601 pages) : illustrations. Digital: text file; PDF.
 Summary

 A brief survey on partial differential equations. Elements of functional analysis. Elliptic equations. The Galerkin finite element method for elliptic problems. Parabolic equations. Generation of 1D and 2D grids. Algorithms for the solution of linear systems. Elements of finite element programming. The finite volume method. Spectral methods. Diffusiontransportreaction equations. Finite differences for hyperbolic equations. Finite elements and spectral methods for hyperbolic equations. Nonlinear hyperbolic problems. NavierStokes equations. Optimal control of partial differential equations. Domain decomposition methods. Reduced basis approximation for parametrized partial differential equations.
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 Quarteroni, Alfio.
 3a ed.  Milan : SpringerVerlag, 2006.
 Description
 Book — xiii, 451 p. : ill.
 Quarteroni, Alfio.
 Oxford : Clarendon Press ; New York : Oxford University Press, 1999.
 Description
 Book — xv, 360 p. : ill. ; 24 cm.
 Summary

 1. Mathematical foundation of domain decomposition methods
 2. Discretized equations and domain decomposition
 3. Iterative domain decomposition methods at the discrete level
 4. Convergence analysis for iterative domain decomposition
 5. Other boundary value problems
 6. Advectiondiffusion equations
 7. Timedependent problems
 8. Heterogeneous domain decomposition methods.
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Science Library (Li and Ma)
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QA377 .Q34 1999  Unknown 
 International Conference on Domain Decomposition (6th : 1992 : Como, Italy)
 Providence, R.I. : American Mathematical Society, 1994.
 Description
 Book — 484 p.
 Summary

 Part I. Theory: Invited Lectures: Domain decomposition methods using modified basis functions by V. I. Agoshkov Uniform convergence estimates for multigrid Vcycle algorithms with less than full elliptic regularity by J. H. Bramble and J. E. Pasciak A threefield domain decomposition methods by F. Brezzi and L. D. Marini Selfadaptive coupling of mathematical models and/or numerical methods by C. Canuto and A. Russo Noniterative domain decomposition for second order hyperbolic problems by C. N. Dawson and T. F. Dupont Some recent results on Schwarz type domain decomposition algorithms by M. Dryja and O. B. Widlund Overlapping domain decomposition methods for parabolic problems by Yu. A. Kuznetsov Domain decomposition and multilevel PCG method for solving $3$$\mathrm{D}$ fourth order problems by J. Sun Some twogrid finite element methods by J. Xu Contributed Lectures Interface conditions for a kind of non linear elliptichyperbolic problems by G. Aguilar and F. Lisbona A domain decomposition for the transport equation by L. Gastaldi Hybrid domain decomposition with unstructured subdomains by J. Mandel Some Schwarz algorithms for the $p$version finite element method by L. F. Pavarino On the robustness and efficiency of the fully adaptive multigrid method by U. Rude Finite volume variational formulation. Application to domain decomposition methods by J.M. Thomas and D. Trujillo Part II. Algorithms: Invited Lectures: Multigrid solvers on decomposed domains by A. Brandt and B. Diskin Domain decomposition preconditioners for convection diffusion problems by T. F. Chan and T. P. Mathew A domain decomposition approach to solving the Helmholtz equation with a radiation boundary condition by O. Ernst and G. H. Golub The dual Schur complement method with wellposed local Neumann problems by C. Farhat and F.X. Roux Implicit domain decomposition algorithms for steady, compressible aerodynamics by W. D. Gropp, D. E. Keyes, and J. S. Mounts A new mixed preconditioning method based on the clustered elementbyelement preconditioners by T. E. Tezduyar, M. Behr, S. K. Aliabadi, S. Mittal, and S. E. Ray Contributed Lectures Domain decomposition methods with local Fourier basis for parabolic problems by A. Averbuch, M. Israeli, and L. Vozovoi A domain decomposition method for the polar factorization of vector fields by J.D. Benamou and Y. Brenier An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation by B. Bialecki, X.C. Cai, M. Dryja, and G. Fairweather An iterative finiteelement collocation method for parabolic problems using domain decomposition by M. C. Curran A domain decomposition method using sparse grids by M. Griebel Domain decomposition for the Stokes equations in streamfunction formulation by W. Heinrichs Overlapping domain decomposition methods for the obstacle problem by Yu. A. Kuznetsov, P. Neittaanmaki, and P. Tarvainen An iteration scheme for nonsymmetric interface operators by C.H. Lai Factorization of the convectiondiffusion operator and a (possibly) non overlapping Schwarz method by F. Nataf and F. Rogier Domain decomposition method coupling finite elements and preconditioned Chebyshev collocation to solve elliptic problems by C. R. Schneidesch, M. O. Deville, and E. H. Mund Additive Schwarz methods and acceleration with variable weights by T.M. Shih, C.B. Liem, and T. Lu Part III. Parallelism: Invited Lectures: Parallel domain decomposition for incompressible fluid dynamics by P. F. Fischer Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods by W. D. Gropp and B. F. Smith Parallel iterative solution of symmetric coupled FE/BEequations via domain decomposition by U. Langer Contributed Lectures Implementation of domain decomposition techniques on nCUBE2 parallel machine by A. Brambilla, C. Carlenzoli, G. Gazzaniga, P. Gervasio, and G. Sacchi A class of domain decomposition preconditioners for massively parallel computers by P. Ciarlet, Jr. and G. Meurant A domain decomposition environment for local time dependent problems by F. Dellagiacoma, S. Paoletti, F. Poggi, and M. Vitaletti A parallel elementbyelement method for largescale computations with $hp$finite elements by S. Foresti, S. Hassanzadeh, and V. Sonnad Part IV. Applications: Invited Lectures: Coupling Boltzmann and Euler equations without overlapping by J. F. Bourgat, P. L. Tallec, B. Perthame, and Y. Qiu On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Application to scattering by M. O. Bristeau, R. Glowinski, and J. Periaux A fictitious domain method for unsteady incompressible viscous flow modelled by NavierStokes equations by R. Glowinski, T.W. Pan, and J. Periaux Contributed Lectures Introduction of domain decomposition techniques in timedependent flow problems by M. C. Ciccoli, J. A. Desideri, and J. Periaux The Schur complement algorithm for the solution of contact problems by Z. Dostal Spectral multidomain methods for the simulation of wave propagation in heterogeneous media by E. Faccioli, A. Quarteroni, and A. Tagliani Domain decomposed preconditioning for faulted geological blocks by A. Gersztenkorn and J. C. Diaz A domain decomposition method for simulating 2D external viscous flows by J.L. Guermond and W.Z. Shen Interface conditions for heterogeneous domain decomposition: Coupling of different hyperbolic systems by I. Lie Simulation of 3D NavierStokes flows via domain decomposition by the modified discrete vector potential model by D. Mansutti and F. Pitolli.
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SAL3 (offcampus storage)
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QA402.2 .I57 1992  Available 
 Quarteroni, Alfio.
 Berlin ; New York : SpringerVerlag, c1994.
 Description
 Book — 543 p.
 Summary

This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method.
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Science Library (Li and Ma)
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QA377 .Q37 1994  Unknown 
 Quarteroni, Alfio, author.
 Cham : Springer, [2015]
 Description
 Book — 1 online resource (xiv, 296 pages) : illustrations (some color).
 Summary

 1 Introduction
 2 Representative problems: analysis and (highfidelity) approximation
 3 Getting parameters into play
 4 RB method: basic principle, basic properties
 5 Construction of reduced basis spaces
 6 Algebraic and geometrical structure
 7 RB method in actions
 8 Extension to nonaffine problems
 9 Extension to nonlinear problems
 10 Reduction and control: a natural interplay
 11 Further extensions
 12 Appendix A Elements of functional analysis.
 Modellistica numerica per problemi differenziali. English
 Quarteroni, Alfio, author.
 Second edition.  Milan ; New York : Springer, [2014]
 Description
 Book — 1 online resource (xix, 656 pages) : illustrations. Digital: text file; PDF.
 Summary

 1 A brief survey of partial differential equations. 2 Elements of functional analysis. 3 Elliptic equations. 4 The Galerkin finite element method for elliptic problems. 5 Parabolic equations. 6 Generation of 1D and 2D grids. 7 Algorithms for the solution of linear systems. 8 Elements of finite element programming. 9 The finite volume method. 10 Spectral methods. 11 Discontinuous element methods (DG and mortar). 12 Diffusiontransportreaction equations. 13 Finite differences for hyperbolic equations. 14 Finite elements and spectral methods for hyperbolic equations. 15 Nonlinear hyperbolic problems. 16 NavierStokes equations. 17 Optimal control of partial differential equations. 18 Domain decomposition methods. 19 Reduced basis approximation for parametrized partial differential equations.
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 Quarteroni, Alfio. Author
 3. ed.  Milan Berlin Heidelberg ; New York : Springer, 2006.
 Description
 Book — 1 online resource (XIII, 451 Seiten) : Illustrationen, Diagramme
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