# Demos

These demos illustrate DOLFINx usage. Starting with Poisson equation is recommended.

## PDEs (introductory)

## PDEs (advanced)

- Mixed formulation for the Poisson equation
- Stokes equations using Taylor-Hood elements
- Divergence conforming discontinuous Galerkin method for the Navier–Stokes equations
- Elasticity using algebraic multigrid
- Cahn-Hilliard equation
- Static condensation of linear elasticity
- Biharmonic equation
- Solving PDEs with different scalar (float) types
- Matrix-free conjugate gradient solver for the Poisson equation
- Solve the Poisson and linearised elasticity equations using pyamg
- HDG scheme for the Poisson equation

## Nonlinear problems

## Mesh generation

## Interpolation, IO and visualisation

## Advanced iterative solvers

## User-defined and advanced finite elements

## List of all demos

- Poisson equation
- Biharmonic equation
- Cahn-Hilliard equation
- Stokes equations using Taylor-Hood elements
- Elasticity using algebraic multigrid
- Mesh generation with Gmsh
- Helmholtz equation
- Static condensation of linear elasticity
- Visualization with PyVista
- Interpolation and IO
- Solving PDEs with different scalar (float) types
- Variants of Lagrange elements
- Creating TNT elements using Basix’s custom element interface
- Electromagnetic scattering from a wire with scattering boundary conditions
- Electromagnetic scattering from a wire with perfectly matched layer condition
- Electromagnetic modal analysis for a waveguide
- Electromagnetic scattering from a sphere (axisymmetric)
- Divergence conforming discontinuous Galerkin method for the Navier–Stokes equations
- Mixed formulation for the Poisson equation
- Solve the Poisson and linearised elasticity equations using pyamg
- HDG scheme for the Poisson equation