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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 HeatExpand
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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.-Expand
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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 thoroughExpand
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Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
This book provides an extensive and critical overview of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. Expand
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Numerical Models for Differential Problems
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but alsoExpand
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Cardiovascular mathematics : modeling and simulation of the circulatory system
This book introduces the most important terms and concepts of cardiovascular physiopathology ,while Chapter 2 illustrates the basic mathematical models for blood flow and biochemical transfer. Expand
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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 reducedExpand
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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 theExpand
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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 weightExpand
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On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels
For the analysis of flows in compliant vessels, we propose an approach to couple the original 3D equations with a convenient 1D model. This multiscal- e strategy allows for a dramatic reduction ofExpand
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