Solving Numerical PDEs: Problems, Applications, Exercises

1. Front Matter

   Pages i-x

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2. Basic Material

   1. Front Matter

      Pages 1-1

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   2. Some fundamental tools

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 3-15

   3. Fundamentals of finite elements and finite differences

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 17-62

3. Stationary Problems

   1. Front Matter

      Pages 63-63

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   2. Galerkin-finite element method for elliptic problems

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 65-146

   3. Advection-diffusion-reaction (ADR) problems

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 147-202

4. Time Dependent Problems

   1. Front Matter

      Pages 203-203

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   2. Equations of parabolic type

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 205-275

   3. Equations of hyperbolic type

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 277-331

   4. Navier-Stokes equations for incompressible fluids

      • Luca Formaggia, Fausto Saleri, Alessandro Veneziani

      Pages 333-391

5. Back Matter

   Pages 393-440

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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.

• partial differential equations

• MOX — Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Italy

  Luca Formaggia, Fausto Saleri

• Department of Mathematics and Computer Science, Emory University, Atlanta, USA

  Alessandro Veneziani

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