โ Scribed by Luca Formaggia, Fausto Saleri, Alessandro Veneziani (auth.)
No coin nor oath required. For personal study only.
This book stems from the long standing teaching experience of the authors in the courses on Numerical Methods in Engineering and Numerical Methods for Partial Differential Equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University of Bergamo (Italy) and Emory University (Atlanta, USA). It aims at introducing students to the numerical approximation of Partial Differential Equations (PDEs). One of the difficulties of this subject is to identify the right trade-off between theoretical concepts and their actual use in practice. With this collection of examples and exercises we try to address this issue by illustrating "academic" examples which focus on basic concepts of Numerical Analysis as well as problems derived from practical application which the student is encouraged to formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the authors in research project developed in collaboration with scientists of different fields (biology, medicine, etc.) and industry. We wanted this book to be useful both to readers more interested in the theoretical aspects and those more concerned with the numerical implementation.
Front Matter....Pages i-x
Front Matter....Pages 1-1
Some fundamental tools....Pages 3-15
Fundamentals of finite elements and finite differences....Pages 17-62
Front Matter....Pages 63-63
Galerkin-finite element method for elliptic problems....Pages 65-146
Advection-diffusion-reaction (ADR) problems....Pages 147-202
Front Matter....Pages 203-203
Equations of parabolic type....Pages 205-275
Equations of hyperbolic type....Pages 277-331
Navier-Stokes equations for incompressible fluids....Pages 333-391
Back Matter....Pages 393-440
Partial Differential Equations; Mathematics, general; Functional Analysis; Numerical Analysis
๐ SIMILAR VOLUMES
This book stems from the long standing teaching experience of the authors in the courses on Numerical Methods in Engineering and Numerical Methods for Partial Differential Equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University
Copyright Page; Preface; Table of Contents; Part I Basic Material; 1 Some fundamental tools; 1.1 Hilbert spaces; 1.2 Distributions; 1.3 The spaces Lp and Hs; 1.4 Sequences in lp; 1.5 Important inequalities; 1.6 Brief overview of matrix algebra; 2 Fundamentals of finite elements and finite differenc
One of the great attractions of mathematics, to its devotees, may be that a well posed problem does in fact have a unique and exact solution. This idea of absolute precision has a sort of beauty that in its own way is unsurpassable. It may also be what frightens away many who feel more comfortable
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment
<p>This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples