#########
Summation
#########

At :math:`\gcs{1}` cell faces:

.. math::

    \sumxf q
    \equiv
    \vat{q}{\frac{1}{2}}
    +
    \vat{q}{\frac{3}{2}}
    +
    \cdots
    +
    \vat{q}{\ngp{1} - \frac{1}{2}}
    +
    \vat{q}{\ngp{1} + \frac{1}{2}}.

At :math:`\gcs{1}` cell centers:

.. math::

    \sumxc q
    \equiv
    \vat{q}{1}
    +
    \vat{q}{2}
    +
    \cdots
    +
    \vat{q}{\ngp{1} - 1}
    +
    \vat{q}{\ngp{1}}.

At :math:`\gcs{2}` cell faces:

.. math::

    \sumyf q
    \equiv
    \vat{q}{\frac{1}{2}}
    +
    \vat{q}{\frac{3}{2}}
    +
    \cdots
    +
    \vat{q}{\ngp{2} - \frac{3}{2}}
    +
    \vat{q}{\ngp{2} - \frac{1}{2}}.

At :math:`\gcs{2}` cell centers:

.. math::

    \sumyc q
    \equiv
    \vat{q}{1}
    +
    \vat{q}{2}
    +
    \cdots
    +
    \vat{q}{\ngp{2} - 1}
    +
    \vat{q}{\ngp{2}}.

At :math:`\gcs{3}` cell faces:

.. math::

    \sumzf q
    \equiv
    \vat{q}{\frac{1}{2}}
    +
    \vat{q}{\frac{3}{2}}
    +
    \cdots
    +
    \vat{q}{\ngp{3} - \frac{3}{2}}
    +
    \vat{q}{\ngp{3} - \frac{1}{2}}.

At :math:`\gcs{3}` cell centers:

.. math::

    \sumzc q
    \equiv
    \vat{q}{1}
    +
    \vat{q}{2}
    +
    \cdots
    +
    \vat{q}{\ngp{3} - 1}
    +
    \vat{q}{\ngp{3}}.