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: 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.

Table of contents
Lecture 1 Course overview; why consider existing software libraries
Lecture 2 A real brief overview of deal.II
Lecture 3 Obtaining and installing deal.II
Lecture 4 The building blocks of a finite element code
Lecture 5 step-1, part 1: Simple meshes
Lecture 6 step-1, part 2: Playing with meshes
Lecture 7 Learning to use modern tools, part 1 – Eclipse: an Integrated Development Environment (IDE), fragment 1
Lecture 8 Learning to use modern tools, part 1 – Eclipse: an Integrated Development Environment (IDE), fragment 2
Lecture 8.01 Learning to use modern tools, part 1 – Eclipse: an Integrated Development Environment (IDE). Update: Direct project setup via CMake
Lecture 9 step-2: Degrees of freedom, sparsity in finite element matrices
Lecture 10 step-3: A first Laplace solver
Lecture 11 Learning to use modern tools, part 2 – Visit: a visualization tool
Lecture 12 A little bit of C++: Templates
Lecture 13 step-4: A dimension-independent Laplace solver
Lecture 14 step-5: Computing on successively refined meshes
Lecture 15 Adaptively refined meshes
Lecture 16 Hanging nodes and other constraints
Lecture 17 step-6: Adaptive meshes
Lecture 18 Debug vs. optimized mode
Lecture 19 Problems with more than one solution variable
Lecture 20 step-20: The mixed Laplace equation
Lecture 21 Block structured solvers for vector-valued problems
Lecture 21.5 Boundary conditions. Part 1: Theory
Lecture 21.55 Boundary conditions. Part 2: Neumann and Robin boundary conditions
Lecture 21.6 Boundary conditions. Part 3a: Homogenous Dirichlet boundary conditions
Lecture 21.65 Boundary conditions. Part 3b: Inhomogenous Dirichlet boundary conditions
Lecture 22 Some data structure design considerations
Lecture 23 Learning to use modern tools, part 3 – doxygen: a documentation tool
Lecture 24 Best programming practices: Defensive programming and other ways to avoid bugs
Lecture 25 More on debugging using Eclipse's built-in debugger
Lecture 26 Time dependent problems: A taxonomy
Lecture 27 Time discretizations for parabolic problems
Lecture 28 Time discretizations for second-order hyperbolic problems
Lecture 29 The step-26 tutorial program -- the heat equation. Part 1: The basics
Lecture 30 The step-26 tutorial program -- the heat equation. Part 2: Adaptive meshes for time dependent problems
Lecture 31 First-order hyperbolic systems
Lecture 31.5 Nonlinear problems, part 1: Introduction
Lecture 31.55 Nonlinear problems, part 2: Newton's method for PDEs
Lecture 31.6 Nonlinear problems, part 3: Newton's method for the minimal surface equation, step-15
Lecture 31.65 Nonlinear problems, part 4: Fixed point/Picard iteration for the minimal surface equation
Lecture 31.7 Nonlinear problems, part 5: Pseudo-time stepping for the minimal surface equation
Lecture 32 Learning to use modern tools, part 4 – Paraview, an alternative visualization tool
Lecture 32.5 Learning to use modern tools, part 5a: Version control systems (VCSs), Subversion
Lecture 32.55 Learning to use modern tools, part 5a1: Version control systems (VCSs), Subversion – undoing, branching and merging
Lecture 32.75 Learning to use modern tools, part 5b: Version control systems (VCSs), git
Lecture 32.8 NEW Learning to use modern tools, part 5b1: Version control systems (VCSs), Using git and github in practice
Lecture 33 Which element to use. Part 1: "Simple" problems
Lecture 33.25 Which element to use. Part 2: Saddle-points problems
Lecture 33.5 Which quadrature formula to use
Lecture 34 What solver to use
Lecture 35 What preconditioner to use — Introduction and Parts 1+2: Simple preconditioners for simple problems
Lecture 37 What preconditioner to use — Part 4: Simple preconditioners for complex problems
Lecture 38 What preconditioner to use — Part 5: Complex ("physics-based"/"block") preconditioners for complex problems
Lecture 39 Parallelization: Introduction
Lecture 40 Parallelization on a single, shared memory machine
Lecture 41 Parallelization on a cluster of distributed memory machines — Part 1: Introduction to MPI
Lecture 41.25 Parallelization on a cluster of distributed memory machines — Part 2: Debugging with MPI
Lecture 41.5 Parallelization on a cluster of distributed memory machines — Part 3: Distributed computing in deal.II and step-40
Lecture 41.75 Parallelization on a cluster of distributed memory machines — Part 4: Parallel solvers and preconditioners
Lecture 42 Beyond computational methods — Part 1: Workflows in scientific computing
Lecture 43 Beyond computational methods — Part 2: Issues with developing large software