FEniCS — The Complete Guide: Free PDE Solving Straight From the Weak Form
FEniCS is an open-source project for solving partial differential equations by the finite element method. Instead of choosing an analysis type from a list, you write the weak (variational) form in the UFL language and the system generates and compiles efficient code. The current generation is called FEniCSx, and its main component is DOLFINx.
FEniCS
FEniCS Project
Solve partial differential equations by writing the variational form directly.
Get it from the vendorWhat you get
- Direct mathematical formulation — the equation in the code looks like the equation in the paper.
- Automatic code generation — matrix assembly runs in fast compiled code.
- A range of elements — high-order Lagrange, mixed elements and more.
- Parallel computing — MPI and PETSc solvers, from a laptop to a cluster.
- Python interface — natural integration with NumPy, notebooks and plotting tools.
Who it suits
Researchers and students whose difficulty is the equations, not the geometry. You need to know weak formulations and Python. The convenient install is through conda or Docker; on Windows most people work through WSL.
Related tools
A similar approach in a dedicated language — FreeFEM. A similar approach with high-order elements and a built-in mesher — NGSolve. For meshing — Gmsh; for viewing results — ParaView.
FreeFEM
Sorbonne Université / Inria
Solves partial differential equations in a language close to the mathematical formulation.
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Netgen / NGSolve — Multiphysics Finite Elements
TU Wien / NGSolve Project
High-order finite element mesher and solver for mechanics, flow and electromagnetics.
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Gmsh
Gmsh Project
FEA mesh generator with built-in geometry and scripting — standard infrastructure for open numerical work.
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ParaView
Kitware / Sandia / Los Alamos
Large-scale simulation post-processing — slices, streamlines and animation.
Get it from the vendorThe bottom line
FEniCS is one of the fastest ways to turn a new equation into a working solution — free, open and used in research worldwide.