.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/WeakForms/Poisson1.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_WeakForms_Poisson1.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_WeakForms_Poisson1.py:


Poisson1
========

Poisson equation with unit load.

Reference: https://scikit-fem.readthedocs.io/en/latest/listofexamples.html#example-1-poisson-equation-with-unit-load

.. GENERATED FROM PYTHON SOURCE LINES 13-64



.. image-sg:: /examples/WeakForms/images/sphx_glr_Poisson1_001.png
   :alt: $u$
   :srcset: /examples/WeakForms/images/sphx_glr_Poisson1_001.png
   :class: sphx-glr-single-img





.. code-block:: Python
   :lineno-start: 14


    from EasyFEA import Display, ElemType, Models, Simulations
    from EasyFEA.fem import Field, BiLinearForm, LinearForm
    from EasyFEA.Geoms import Domain

    if __name__ == "__main__":
        Display.Clear()

        # ----------------------------------------------
        # Mesh
        # ----------------------------------------------

        contour = Domain((0, 0), (1, 1), 1 / 2**6)

        mesh = contour.Mesh_2D([], ElemType.TRI3, isOrganised=True)

        nodes = mesh.Nodes_Tags(["L0", "L1", "L2", "L3"])

        # ----------------------------------------------
        # Formulations
        # ----------------------------------------------

        field = Field(mesh.groupElem, 1)

        @BiLinearForm
        def bilinear_form(u: Field, v: Field):
            return u.grad.dot(v.grad)

        @LinearForm
        def linear_form(v: Field):
            return 1.0 * v

        weakForms = Models.WeakForms(field, computeK=bilinear_form, computeF=linear_form)

        # ----------------------------------------------
        # Simulation
        # ----------------------------------------------

        simu = Simulations.WeakFormSimu(mesh, weakForms)

        simu.add_dirichlet(nodes, [0], ["u"])

        simu.Solve()

        # ----------------------------------------------
        # Results
        # ----------------------------------------------

        Display.Plot_Result(simu, "u")

        Display.plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.231 seconds)


.. _sphx_glr_download_examples_WeakForms_Poisson1.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: Poisson1.ipynb <Poisson1.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: Poisson1.py <Poisson1.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: Poisson1.zip <Poisson1.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_