FEniCS Notes

This repository contains a collection of notes on FEniCS using Jupyter Notebooks, which teach how to use finite element methods to solve PDEs and to solve difficult linear systems from PDE discretizations using FEniCS. These notes are under construction. They will cover the following topics:

• Fundamentals of finite element methods
• Modeling linear and nonlinear elasticity
• Solving the heat equation
• Solving incompressible Navier-Stokes equations
• Mixed finite element formulations for Stokes equations
• Advection-diffusion-reaction equations coupled with Navier-Stokes equations
• Convection-diffusion equations
• Generating meshes
• Specifying boundary conditions
• Controlling iterative solvers

Most of the materials were adapted from the FEniCS Tutorial the FEniCS Book, and the FEniCS demos. However, they have been rearranged and expanded for teaching and research at Stony Brook University.

To study the Notebooks, here is the recommended sequence:

1. Fundamentals - Poisson equations
   • Case study: deflection of a membrane using Poisson equations
2. Modeling linear elasticity
3. Solving the heat equation
4. Solving nonlinear problems
   • A nonlinear Poisson equation
   • Hyperelasticity
5. Solving incompressible Navier-Stokes equations
   • Case study: Navier-Stokes for a cylinder
6. Mixed finite element formulations for Stokes equations
   • Stokes equations with Stabilized first-order finite elements
7. Advection-diffusion-reaction equations coupled with Navier-Stokes equations
8. Galerkin method with least-squares stablization for Convection-dominant equations

To run these notebooks interactively, use the ams529_jupyter.py script at https://github.com/compdatasci/ams529-desktop.