Solving Numerical PDEs Problems, Applications, Exercises [Paperback]

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.

Written from years of teaching experience, this volume introduces students to the numerical approximation of Partial Differential Equations (PDEs). The text presents examples and exercises that focus on basic concepts of numerical analysis, as well as problems derived from practical application.

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 differences. 2.1 The one dimensional case: approximation by piecewise polynomials. 2.2 Interpolation in higher dimension using finlc7