Starting in the spring 2013, I videotaped the lectures
for my *MATH 676: Finite element methods in scientific
computing* course
at the KAMU TV studio at
Texas A&M. These are lectures
on many aspects of scientific computing, software,
and the practical aspects of the finite element method, as
well as their implementation in the
deal.II software library. Support
for creating these videos was also provided by the
National Science Foundation and
the Computational
Infrastructure in Geodynamics.

The videos are part of a broader effort to develop a modern way of teaching Computational Science and Engineering (CS&E) courses. If you are interested in adapting our approach, you may be interested in this paper I wrote with a number of education researchers about the structure of such courses and how they work.

**Note 1:** In some of the videos, I demonstrate code or user
interfaces. If you can't read the text, change the
video quality by clicking on the "gear" symbol at the
bottom right of the YouTube player.

**Note 2:**
deal.II is an
actively developed library, and in the course of this
development we occasionally deprecate and remove
functionality. In some cases, this implies that we also
change tutorial programs, but the nature of videos is that
this is not reflected in something that may have been
recorded years ago. If in doubt, consult
the *current* version of the tutorial.

**Lecture 33: Which element to use. Part 1: "Simple" problems**

We use many different kinds of finite elements, depending on the equations we want to solve. For example, we may use the usual Lagrange elements for the Laplace equation, but we use Taylor-Hood elements for Stokes, Raviart-Thomas elements for the mixed Laplace, and Nedelec elements for the Maxwell equations. Then there is also a veritable zoo of the BDM, BDDM, ABW, ABF, Rannacher-Turek, Crouzeix-Raviart, and many other elements.

This first of two lectures discusses what elements one chooses for "simple" problems, and which element orders one typically wants to use.

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**Slides:** click here