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 31.55: Nonlinear problems, part 2: Newton's method for PDEs**

Newton's method is the most method of choice to solve nonlinear equations (at least for problems for which it converges) because it converges with quadratic order. In the context of PDEs, we need to derive the equations that describe the Newton update as the solutions of a particular, linearized version of the original PDE.

This lecture shows how this is done for our model problem, the minimal surface equation, and discusses some of the other practical aspects of Newton's method in the context of PDEs.

**Slides:** click here