A. Quarteroni

Publications609
h-index73
Citations27,985
Highly Influential Citations1,176
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Spectral methods for fluid dynamics
1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat…
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Spectral Methods: Fundamentals in Single Domains
Polynomial Approximation.- Basic Approaches to Constructing Spectral Methods.- Algebraic Systems and Solution Techniques.- Polynomial Approximation Theory.- Theory of Stability and Convergence.-…
Numerical Approximation of Partial Differential Equations
This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough…
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Reduced Basis Methods for Partial Differential Equations: An Introduction
1 Introduction.- 2 Representative problems: analysis and (high-fidelity) approximation.- 3 Getting parameters into play.- 4 RB method: basic principle, basic properties.- 5 Construction of reduced…
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Numerical Models for Differential Problems
TLDR
This text considers the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems.
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Cardiovascular mathematics : modeling and simulation of the circulatory system
TLDR
This book provides a set of well described and reproducible test cases and applications of cardiovascular physiopathology, focusing on the main characteristics of the different flow regimes encountered in the cardiovascular system.
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
TLDR
This book provides an extensive and critical overview of the essential algorithmic and theoretical aspects of spectral methods for complex geometries, in addition to detailed discussions of spectral algorithms for fluid dynamics in simple and complexGeometries.
One-dimensional models for blood flow in arteries
In this paper a family of one-dimensional nonlinear systems which model the blood pulse propagation in compliant arteries is presented and investigated. They are obtained by averaging the…
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Approximation results for orthogonal polynomials in Sobolev spaces
We analyze the approximation properties of some interpolation operators and some L2-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight…
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On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels
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