Source code for fe_utils.solvers.mastery

"""Solve a nonlinear problem using the finite element method.
If run as a script, the result is plotted. This file can also be
imported as a module and convergence tests run on the solver.
"""
from argparse import ArgumentParser


def solve_mastery(resolution, analytic=False, return_error=False):
    """This function should solve the mastery problem with the given
    resolution. It should return both the solution
    :class:`~fe_utils.function_spaces.Function` and the :math:`L^2` error in
    the solution.

    If ``analytic`` is ``True`` then it should not solve the equation
    but instead return the analytic solution. If ``return_error`` is
    true then the difference between the analytic solution and the
    numerical solution should be returned in place of the solution.
    """

    raise NotImplementedError
    # return (u, p) error


if __name__ == "__main__":

    parser = ArgumentParser(
        description="""Solve the mastery problem.""")
    parser.add_argument(
        "--analytic", action="store_true",
        help="Plot the analytic solution instead of solving the finite"
        " element problem.")
    parser.add_argument("--error", action="store_true",
                        help="Plot the error instead of the solution.")
    parser.add_argument(
        "resolution", type=int, nargs=1,
        help="The number of cells in each direction on the mesh."
    )
    args = parser.parse_args()
    resolution = args.resolution[0]
    analytic = args.analytic
    plot_error = args.error

    u, error = solve_mastery(resolution, analytic, plot_error)

    u.plot()