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 30.25: Time discretizations for advection-diffusion and other problems: IMEX, operator splitting, and other ideas**

Having looked at (explicit and implicit) time discretizations for time dependent model problems in the last few lectures, I turn to the question of what to do in slightly more complicated cases where the equation is not either clearly hyperbolic or parabolic. In fact, in reality many equations lie somewhere on a spectrum, depending on whether transport or diffusion are the dominant factors, and we may have to treat the respective terms differently. In other cases, equations are coupled or simply have a completely different structure.

This lecture then is about what to do in such situations, and introduces a few ideas that explain how one approaches such cases. In particular, I introduce IMEX (implicit-explicit) and operater splitting schemes (e.g., the "Lie" and "Strang" splitting methods). I then also discuss a number of ways how one can increase the accuracy of these methods without too much additional effort.

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**Slides:** click here