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Introduction to finite element methods
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:Authors: Hans Petter Langtangen
:Date: Oct 31, 2014

**PRELIMINARY VERSION**

The finite element method is a powerful tool for solving differential
equations. The method can easily deal with complex geometries and
higher-order approximations of the solution.
Figure :ref:`fem:motivation:fig:dolfin` shows
a two-dimensional domain with a non-trivial geometry. The idea is to
divide the domain into triangles (elements) and seek a polynomial approximations
to the unknown functions on each triangle. The method glues these
piecewise approximations together to find a global solution.
Linear and quadratic polynomials over the triangles are particularly
popular.

.. _fem:motivation:fig:dolfin:

.. figure:: dolfin_mesh.png
   :width: 400

   *Domain for flow around a dolphin*