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 31.5: Nonlinear problems, part 1: Introduction

Correct descriptions of the real world are all nonlinear. The linear equations we have considered so far are only approximations where we have made the assumption that something is small and, consequently, terms that involve the square of the solution or higher powers can be neglected.

This lecture gives an overview of nonlinear equations, introduces the (nonlinear) minimal surface equation as a concrete example, and the presents general strategies that are used to solve them. The next lecture then looks at the practical implementation of a method to solve the minimal surface equation in step-15.

Slides: click here