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Numerical Models for Differential Problems (MS&A), by Alfio Quarteroni
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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 also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
- Sales Rank: #3283107 in Books
- Published on: 2014-01-14
- Original language: English
- Number of items: 1
- Dimensions: 9.54" h x 1.36" w x 6.32" l, 2.85 pounds
- Binding: Hardcover
- 658 pages
About the Author
The Author is Professor and Director of the Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998, Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989, and Scientific Director of MOX, since 2002. Author of 22 books published with Springer, and of about 200 papers published in refereed international Journals, Conference Proceedings and Magazines, Alfio Quarteroni is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC.
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An important theoretical reference to Galekin methods for PDEs
By Simone Marras
Written by one of the leading figures in the field of variational methods and numerical mathematics, this book is an invaluable reference for graduate students and researchers working in the field of Galerkin methods. It is written by a mathematician, with the formalism proper of a mathematician; it may thus appear somewhat cumbersome if the reader is seeking an applied insight of the finite element method. However, the inclined engineer/scientist/mathematician will find its formalism an important ingredient to deeply understand the theory behind the method, although built in a very understandable language.
The books covers different types of Galerkin schemes, with special attention to finite elements and spectral elements, and a bit on the finite volume and finite difference methods. It should be considered by those who are willing to make an intellectual effort to understanding the theory of finite elements, but should be avoided by those expecting a book that could help with their practical implementation --some implementation issues are introduced in the context of object-oriented programming, but it may not be enough for beginners. This is the translation of the original Italian edition: Modellistica Numerica per Problemi Differenziali.
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