fenics-fem

What problem does it solve?

This Skill helps you solve partial differential equations on complex geometries by formulating them in weak form and computing finite element solutions with FEniCS/dolfinx.

Core Features & Use Cases

• Weak-form FEM setup: Derives and implements variational formulations (e.g., Poisson, elasticity, Stokes, heat equation) directly in dolfinx/ufl.
• Meshes from code and gmsh: Generates meshes with dolfinx (unit squares/rectangles) or creates CAD-based domains (e.g., annuli with holes) using gmsh for robust geometry handling.
• Boundary conditions and solvers: Applies Dirichlet/Neumann-style setups via geometric dof location and uses PETSc-backed linear solvers for reliable assembly/solution.
• Visualization-ready outputs: Exports solutions to XDMF so you can inspect fields in ParaView (including post-processed quantities like von Mises stress).

Quick Start

Use this Skill to solve a Poisson problem on a unit square with a manufactured solution and then run a convergence study to quantify L2 and H1 errors.