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  • Book
  • Open Access
  • © 2016

Solving PDEs in Python

The FEniCS Tutorial I

  • Definitive and authoritative guide to FEniCS programming

  • Revised, expanded and improved version of the very popular FEniCS Tutorial chapter that many users have enjoyed for the last 5 years

  • Teaches how to program advanced finite element solvers for challenging applications in just minutes, including basic Python programming, finite element methodology and its application to a range of fundamental PDE models

  • Comes with a series of example programs that demonstrate fundamental techniques

  • Can be used as a starting point for readers who want to implement their own PDE solvers

  • Includes supplementary material:

Part of the book series: Simula SpringerBriefs on Computing (SBRIEFSC, volume 3)

Buying options

Softcover Book USD 24.99
Price excludes VAT (USA)

Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
  2. Preliminaries

    • Hans Petter Langtangen, Anders Logg
    Pages 3-10Open Access
  3. Fundamentals: Solving the Poisson equation

    • Hans Petter Langtangen, Anders Logg
    Pages 11-35Open Access
  4. A Gallery of Finite Element Solvers

    • Hans Petter Langtangen, Anders Logg
    Pages 37-81Open Access
  5. Subdomains and boundary conditions

    • Hans Petter Langtangen, Anders Logg
    Pages 83-107Open Access
  6. Extensions: Improving the Poisson Solver

    • Hans Petter Langtangen, Anders Logg
    Pages 109-141Open Access
  7. Back Matter

    Pages 143-148

About this book

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs.

This book is open access under a CC BY license.


  • Finite element
  • FEniCS
  • Partial Differential Equations
  • Python
  • Simulation
  • Open access


“This book of about 150 pages introduces the FEniCS software toolset in 5 chapters ... . The targeted audience includes applications scientists in the area of PDEs who seek for an easy way to implement their problems, and who are willing to invest the time to learn how to work with FEniCS.” (Gudula Rünger, zbMATH 1376.65144, 2018)

Authors and Affiliations

  • Center for Biomedical Computing, Simula Research Laboratory, Center for Biomedical Computing, Fornebu, Norway

    Hans Petter Langtangen

  • Dept. Mathematics, Chalmers University of Technologym Department of Mathematics, Göteborg, Sweden

    Anders Logg

Bibliographic Information

Buying options

Softcover Book USD 24.99
Price excludes VAT (USA)