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The FEniCSx tutorial

Introduction

An overview of the FEniCS Project
Changelog

Fundamentals

Solving the Poisson equation
- Implementation
The Poisson problem with complex numbers
Weak imposition of Dirichlet conditions for the Poisson problem
Deflection of a membrane
- Implementation
- Using Paraview for visualization

A Gallery of finite element solvers

A Gallery of finite element solvers
The heat equation
- Diffusion of a Gaussian function
- A known analytical solution
Singular Poisson problem
A nonlinear Poisson equation
- Implementation
The equations of linear elasticity
- Implementation
- Scaling
The Navier-Stokes equations
- Test problem 1: Channel flow (Poiseuille flow)
- Test problem 2: Flow past a cylinder (DFG 2D-3 benchmark)
Hyperelasticity
The Helmholtz equation
- Implementation
Adaptive mesh refinement with NetGen and DOLFINx

Subdomains and boundary conditions

Combining Dirichlet and Neumann conditions
Setting multiple Dirichlet condition
Defining subdomains for different materials
Setting multiple Dirichlet, Neumann, and Robin conditions
Component-wise Dirichlet BC
Electromagnetics example

Improving your FEniCSx code

Mixed Poisson with a Schur complement pre-conditioner
Solver configuration
JIT options and visualization using Pandas
Error control: Computing convergence rates
Custom Newton solvers

Repository
Open issue

Index

By Jørgen S. Dokken

Last updated on Mar 23, 2026.

This webpage is an adaptation of The FEniCS tutorial and is distributed under the terms of the Creative Commons Attribution 4.0 International License which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.