Course Information

Day One Handout

The course meets in slot 19, from 2:00-3:15 PM on Tuesdays and Thursdays, in HH 3015. My office hours are on Mondays and Thursdays from 10:00 - noon, in HH-2019, or by appointment.

No textbooks are required for this course. Relevant e-books from the library's collection (or elsewhere) include:

  • Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by Leveque
  • A First Course in the Numerical Analysis of Differential Equations by Iserles
  • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen
  • Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory by Braess
  • Finite Volume Methods by Eymard, Gallouët, and Herbin
  • Iterative methods for sparse linear systems by Saad (full text pdf available here)

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

  • 9/8: Introduction; Taylor's theorem and differencing
  • 9/13: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions
  • 9/15: 2D meshes and differencing, approximating DEs
  • 9/20: Convergence Theory, HW1 Due, HW2 Distributed, Solutions
  • 9/22: Convergence Theory, continued
  • 9/27: Boundary conditions, HW2 Due, HW3 Distributed, Solutions, Matlab routines for HW3: FD Code, Uniform-mesh driver, Random-mesh driver
  • 9/29: Boundary conditions continued, complications
  • 10/4: Meshless Finite Differences, HW3 Due, HW4 Distributed, Solutions, Matlab routines for HW4: Driver, O(h) routine, O(h^2) routine
  • 10/6: Weak forms and Ritz-Galerkin
  • 10/11: Fall Break, no lecture
  • 10/13: Approximation Theory, HW4 Due
  • 10/18: Piecewise linears
  • 10/20: Midterm Exam, Solutions
  • 10/25: Piecewise polynomial approximation, HW5 Distributed, Solutions, Matlab routines for HW5: Driver, solution routine
  • 10/27: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma
  • 11/1: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW6 Distributed, Solutions
  • 11/3: Finite elements in 2D and 3D, approximation properties, HW5 Due
  • 11/8: Finite volumes in 1D, HW7 Distributed, Solutions
  • 11/10: Finite volumes in 2D and 3D, HW6 Due
  • 11/15: Spectral Methods, HW8 Distributed, Solutions, Fast Poisson Solver code and driver, Spectral Method code and driver
  • 11/17: Fast Fourier Transform and Fast Poisson Solver, HW9 Distributed, Solutions, Jacobi, Gauss-Seidel, matrix, and driver routines, HW7 Due
  • 11/22: Direct Methods
  • 11/24: Iterative Methods and Matrix Splitting, HW8 Due
  • 11/29: Krylov Methods and GMRES
  • 12/1: MINRES and CG, HW9 Due
  • 12/8: Final Exam, 9-11am, HH3017