Convergence square

This case validates convergence using an analytical harmonic solution on a square domain.

1. Running the case

mpirun -np 4 feelpp_toolbox_electric --case "github:{path:toolboxes/electric/cases/convergence-square}" --case.config-file 2d.cfg
Case option
--case "github:{path:toolboxes/electric/cases/convergence-square}"
Case config file option
--case.config-file 2d.cfg

2. Model setup

  • Dimension: 2D

  • Material: sigma = 1

  • Boundary condition: exact Dirichlet value on all boundaries (Vexact)

  • Postprocess: Norm measures (L2-error, H1-error) with checkers

3. Exact solution

\[V(x,y) = e^x \cos(y)\]

The case computes norm errors and verifies expected finite-element convergence behavior.