# Source code for pymordemos.elliptic_unstructured

```#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2019 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

"""Simple demonstration of solving the Poisson equation in 2D on a circular sector
domain of radius 1 using an unstructured mesh.

Note that Gmsh (http://geuz.org/gmsh/) is required for meshing.

Usage:
elliptic_unstructured.py ANGLE NUM_POINTS CLSCALE

Arguments:
ANGLE        The angle of the circular sector.
NUM_POINTS   The number of points that form the arc of the circular sector.
CLSCALE      Mesh element size scaling factor.

Options:
-h, --help   Show this message.
"""

from docopt import docopt
import numpy as np

from pymor.analyticalproblems.elliptic import StationaryProblem
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.domaindescriptions.polygonal import CircularSectorDomain
from pymor.functions.basic import ConstantFunction, ExpressionFunction

[docs]def elliptic_gmsh_demo(args):
args['ANGLE'] = float(args['ANGLE'])
args['NUM_POINTS'] = int(args['NUM_POINTS'])
args['CLSCALE'] = float(args['CLSCALE'])

problem = StationaryProblem(
domain=CircularSectorDomain(args['ANGLE'], radius=1, num_points=args['NUM_POINTS']),
diffusion=ConstantFunction(1, dim_domain=2),
rhs=ConstantFunction(np.array(0.), dim_domain=2, name='rhs'),
dirichlet_data=ExpressionFunction('sin(polar(x)[1] * pi/angle)', 2, (),
{}, {'angle': args['ANGLE']}, name='dirichlet')
)

print('Discretize ...')
m, data = discretize_stationary_cg(analytical_problem=problem, diameter=args['CLSCALE'])
grid = data['grid']
print(grid)
print()

print('Solve ...')
U = m.solve()

solution = ExpressionFunction('(lambda r, phi: r**(pi/angle) * sin(phi * pi/angle))(*polar(x))', 2, (),
{}, {'angle': args['ANGLE']})
U_ref = U.space.make_array(solution(grid.centers(2)))

m.visualize((U, U_ref, U-U_ref),
legend=('Solution', 'Analytical solution (circular boundary)', 'Error'),
separate_colorbars=True)

if __name__ == '__main__':
args = docopt(__doc__)
elliptic_gmsh_demo(args)
```