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 29: The step-26 tutorial program -- the heat equation. Part 1: The basics

In this lecture, I look at the practical realization of an implicit time stepping method for the heat equation, using the step-26 tutorial program. This lecture covers the basic approach: how to do the time stepping, what we can expect from the matrix that needs to be inverted in every time step, and how one, in practice, evaluates a complex expression on the right hand side. It then takes a look at the basic structure of a time dependent solver program, both in terms of member variables in the main class and how the usual run() function now looks.

Slides: click here