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.
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 26: Time dependent problems: A taxonomy
Time dependent problems come in all sorts of kinds and forms but by and large they can be sorted into three big classes: parabolic, hyperbolic second order, and hyperbolic first order equations. While many equations do not satisfy the strict criteria to be of these three kinds, most in fact at least "morally" satisfy what makes us think of being in one class or another.
In this lecture, I look at a few of them and explain their characteristics. I then look at the two fundamental ways one can approach discretizing time dependent problems: The "method of lines" and the "Rothe method".
Slides: click here