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 31.65: Nonlinear problems, part 4: Fixed point/Picard iteration for the minimal surface equation

An alternative to using Newton's method for nonlinear problems is to use a simple fixed point (or "Picard") iteration. This lecture shows how this looks looks like for our model problem, the minimal surface equation (MSE). I then take step-6 and modify it in such a way that it solves the MSE instead. The necessary modifications turn out to be surprisingly simple.

Slides: click here