DUNE-fem

Discontinuous Galerkin methods and adaptive meshes.

Install

pip install dune-fem mpi4py

mpi4py is a hidden requirement: without it the first import stops with "Please run pip install mpi4py before rerunning your Dune script."

Then check that openPASO sees it:

python check_install.py

What openPASO knows for DUNE-fem

17 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 residual error estimator	2-D	2d
dg_advection	DG method for pure advection equation (upwind flux)	2-D	2d
dg_advection_diffusion	Steady advection-diffusion with upwind flux and SIPG diffusion on triangles	2-D	2d
eigenvalue	Eigenvalue problem -Δu = λu via shift-invert inverse iteration	2-D	2d
heat	Steady heat conduction (UFL)	2-D	2d
helmholtz	Helmholtz equation -Δu - k²u = f with MMS verification	2-D	2d
hyperelasticity	Neo-Hookean finite-strain hyperelasticity with automatic Newton via UFL	2-D	2d
linear_elasticity	Linear elasticity (UFL vector space)	2-D	2d
maxwell	Maxwell equations: 2-D TE-mode scalar Helmholtz proxy (-Δu - k²u = f); full H(curl) via NGSolve	2-D	2d
mixed_methods	Mixed Poisson with Raviart-Thomas RT0 flux and DG-P0 pressure (H(div) x L²)	2-D	2d
navier_stokes	Incompressible Navier-Stokes via Picard iteration (lid-driven cavity)	2-D	2d
nonlinear	Nonlinear PDE via Newton method (UFL)	2-D	2d
poisson	Poisson equation -Δu = f (UFL forms, DUNE backend)	2-D, 3-D	2d
poisson_mms	3D variable-coefficient Poisson manufactured-solution (MMS) convergence family — -div(kappa grad u) = f on [0,L]^3, affine kappa, exact Dirichlet data, uniform refinement with per-level L2/H1 error lines; theoretical L2 order k+1 / H1 order k	3-D	3d_varcoeff
reaction_diffusion	Reaction-diffusion (transient)	2-D	2d
stokes	Stokes flow with Uzawa iteration (UFL)	2-D	2d
time_dependent_heat	Transient heat du/dt - alpha*Δu = f via implicit Euler time-stepping	2-D	2d