scikit-fem

Pure Python, and the easiest to start with. You see and control every step of the assembly.

Install

pip install scikit-fem

Installs in seconds into openPASO's own .venv.

Then check that openPASO sees it:

python check_install.py

What openPASO knows for scikit-fem

22 kinds of problem. Ask for any of them in plain words; the names below are what the model uses internally.

Physics	Description	Dimensions	Templates
adaptive_poisson	h-adaptive Poisson with Babuška-Rheinboldt residual estimator on L-shape (canonical re-entrant-corner test)	2-D	2d
biharmonic	Biharmonic / Kirchhoff plate bending (Morley element)	2-D	2d
contact	Linearized frictionless contact between a 2D elastic block and a rigid foundation, via Picard iteration on the active set. Matches scikit-fem ex04.	2-D	2d
convection_diffusion	Convection-diffusion (SUPG or DG interior penalty)	2-D	2d
dg_methods	Discontinuous Galerkin for advection using ElementDG and InteriorFacetBasis	2-D	2d
eigenvalue	Eigenvalue problems (Laplace, elasticity) via scipy eigsh	2-D	2d
heat	Steady heat conduction	2-D	2d, 2d_steady
heat_transient	Time-dependent heat equation with backward Euler	2-D	2d
helmholtz	Helmholtz equation -Δu - k²u = f with complex arithmetic and absorbing BC	2-D	2d
hydraulic_resistance	Stokes flow through a 2D rectangular channel; computes resistance R=ΔP/Q against the Poiseuille closed-form 12μL/H³. Matches scikit-fem ex29.	2-D	2d
hyperelasticity	Neo-Hookean hyperelasticity with Newton iteration (manual assembly)	2-D	2d
linear_elasticity	Linear elasticity (plane strain)	2-D	2d
mixed_poisson	Mixed Poisson with Raviart-Thomas + DG (flux-conservative)	2-D	2d
navier_stokes	Navier-Stokes flow with Newton iteration (Taylor-Hood P2/P1)	2-D	2d
nonlinear	Nonlinear PDE with Newton iteration (manual Newton loop)	2-D	2d
point_source	Poisson with Dirac-delta point source — discrete RHS is N_i(x0) (Kronecker e_node for mesh-coincident source). Matches scikit-fem ex17 + ex38.	2-D	2d
poisson	Poisson equation -Δu = f (assembly-level)	2-D, 3-D	2d, 2d_tri, 3d
reaction_diffusion	Reaction-diffusion system (Schnakenberg/Turing patterns) with Newton time-stepping	2-D	2d
schrodinger	1D stationary Schrödinger eigenvalue problem -½ψ'' + V(x)ψ = Eψ. Default quantum harmonic oscillator V=½x² with analytic E_n = n+½. Matches scikit-fem ex39.	1-D	1d
stokes	Stokes flow with Taylor-Hood P2/P1 or Mini element	2-D	2d
time_dependent	General time-dependent PDE with theta-method (backward Euler / Crank-Nicolson)	2-D	2d
wave	2D scalar wave equation u_tt - c^2 Δu = 0 with explicit central-difference time integration and lumped mass (no per-step linear solve)	2-D	2d