Course Information

Day One Handout

The course meets in slot 08, from 3:00-3:50 PM on Mondays, Wednesdays, and Fridays, in HH 3017. My office hours are from 1-2PM on Mondays, 11AM - noon on Wednesdays, and 1-2PM on Fridays, in HH-2019.

Textbook
No textbooks are required for this course. Relevant material will be linked below.

D2L
This course will not be using D2L; all material online will be posted here.

Approximate Schedule



  • 1/5: Introduction, Stokes and Navier-Stokes Equations
  • 1/7: Discretization of the Navier-Stokes Equations
  • 1/9: Marker-and-Cell (MAC) discretization
  • 1/12: Discretization matrices
  • 1/14: Pressure-Correction methods
  • 1/16: Direct versus Iterative Methods
  • 1/19: Jacobi and Gauss-Seidel
  • 1/21: Incomplete Factorizations, HW1 distributed, navierstokes.m
  • 1/23: Polynomial Methods
  • 1/26: Arnoldi Algorithm and GMRES
  • 1/28: Lanczos and Conjugate Gradient
  • 1/30: Cost of CG; analyzing Jacobi
  • 2/2: Coarse-grid correction, two-grid algorithm
  • 2/4: Multigrid and the V-cycle, HW1 due
  • 2/6: Multigrid cycling
  • 2/9: How effective is Multigrid?
  • 2/11: Preconditioning
  • 2/13: Midterm Exam
  • 2/16: No class: Winter Semester Break
  • 2/18: No class: Winter Semester Break
  • 2/20: Elliptic PDEs and weak forms, HW2 distributed, fivept.m
  • 2/23: Ritz-Galerkin approximation and error-estimates
  • 2/25: Linear finite elements on [0,1]
  • 2/27: Error estimates and element matrices
  • 3/2: Function spaces and norms, Project proposals due
  • 3/4: Lp and Sobolev spaces
  • 3/6: Hilbert Spaces, Dual Spaces, and Riesz Representation, HW2 Due
  • 3/9: Riesz Representation, Coercivity and continuity
  • 3/11: Lax-Milgram and Céa's Lemmas
  • 3/13: Poincaré-Friedrichs Inequality, element choice
  • 3/16: SNOW DAY
  • 3/18: Approximation properties; non-elliptic problems, HW3 distributed
  • 3/20: Least-Squares finite elements
  • 3/23: No class
  • 3/25: No class
  • 3/27: Finite elements for H(div) and H(curl)
  • 3/30: Finite elements for the Stokes Equations
  • 4/1: Final Exam
  • 4/1: Final Project presentations
  • 4/2: Written Final Project Reports due, HW3 Due