Numerical Approximation of Partial Differential Equations (original) (raw)

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Authors:

  1. Alfio Quarteroni
    1. École Polytechnique Fédérale de Lausanne Chaire de Modelisation et Calcul Scientifique (CMCS), Lausanne, Switzerland
      Politecnico di Milano, MOX, Milan, Italy
  2. Alberto Valli
    1. Dipartimento di Matematica, Università di Trento, Povo TN, Italy

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About this book

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), 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 our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov­ Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel­ oped for the spatial discretization. This theory is then specified to two numer­ ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg­ endre and Chebyshev expansion).

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Table of contents (14 chapters)

  1. Basic Concepts and Methods for PDEs’ Approximation

  2. Approximation of Boundary Value Problems

  3. Approximation of Initial-Boundary Value Problems

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Reviews

"...The book is excellent and is addressed to post-graduate students, research workers in applied sciences as well as to specialists in numerical mathematics solving PDE. Since it is written very clearly, it would be acceptable for undergraduate students in advanced courses of numerical mathematics. Readers will find this book to be a great pleasure."--MATHEMATICAL REVIEWS

Authors and Affiliations

Alfio Quarteroni

Alfio Quarteroni

Alberto Valli

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