Solving Numerical PDEs: Problems, Applications, Exercises

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Springer Science & Business Media, Apr 5, 2012 - Mathematics - 434 pages
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.
 

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Contents

1 Some fundamental tools
3
2 Fundamentals of finite elements and finite differences
16
Part II Stationary Problems
63
3 Galerkinfinite element method for elliptic problems
65
4 Advectiondiffusionreaction ADR problems
147
Part III Time Dependent Problems
203
5 Equations of parabolic type
204
6 Equations of hyperbolic type
277
7 NavierStokes equations for incompressible fluids
332
Part IV Appendices
392
A The treatment of sparse matrices
393
B Whos who
417
References
425
Subject Index
430
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