Numerical Models for Differential Problems

ISBN-13: 9788847058835 / Angielski / Miękka / 2016 / 658 str.

Alfio Quarteroni

Opis

This book introduces the basic concepts for the numerical modelling of partial differential equations. It details algorithmic and computer implementation aspects and provides a number of easy-to-use programs.

Spis treści

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 Diffusion-transport-reaction equations.- 13 Finite differences for hyperbolic equations.- 14 Finite elements and spectral methods for hyperbolic equations.- 15 Nonlinear hyperbolic problems.- 16 Navier-Stokes equations.- 17 Optimal control of partial differential equations.- 18 Domain decomposition methods.- 19 Reduced basis approximation for parametrized partial differential equations.

O autorze

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.