| Class | Date | Main Topic | References |
| 1 | We 09/01 | Overview: Math 621 in a nutshell | Gobbert (SISC) |
| Mo 09/06 | Labor Day | ||
| We 09/08 | 12:00-01:00, ENGR 122: CIRC Software workshop: Basic MATLAB | ||
| 2, #1 | We 09/08 | Prototype problems for elliptic, parabolic, and hyperbolic PDEs | Evans (Ch. 1 and 2) |
| 3 | Mo 09/13 | The finite difference method for elliptic problems | Gobbert (Notes) |
| 4 | We 09/15 | Linear solvers and Matlab programming | |
| 5, #2 | Mo 09/20 | Idea of the finite element method for elliptic problems | |
| We 09/22 | 12:00-01:00, ENGR 122: CIRC Software workshop: Basic Programming in MATLAB | ||
| 6 | We 09/22 | Weak derivatives and Sobolev spaces | Braess (Sec. II.1) |
| 7 | Mo 09/27 | The weak form of elliptic PDEs | Braess (Sec. II.2) |
| 8 | We 09/29 | Galerkin orthogonality and Céa's lemma, standard finite elements | Braess (Sec. II.4, II.5) |
| 9, #3 | Mo 10/04 | Approximation theory and convergence of the FEM in the H1- and L2-norms | Braess (Sec. II.6-II.7) |
| We 10/06 | 12:00-01:00, ENGR 122: CIRC Software workshop: COMSOL Multiphysics | ||
| 10 | We 10/06 | Introduction to COMSOL Multiphysics: GUI | Gobbert (COMSOL) |
| 11 | Mo 10/11 | Introduction to COMSOL Multiphysics: parameter studies | |
| 12 | We 10/13 | Demonstration of the CAD facilities of COMSOL Multiphysics | |
| 13, #4 | Mo 10/18 | Analysis of FEM convergence in COMSOL Multiphysics | Trott & Gobbert (COMSOL 2010) |
| We 10/20 | 12:00-01:00, ENGR 122: CIRC Software workshop: MATLAB 3-D Graphics | ||
| 14 | We 10/20 | The method of lines for a parabolic prototype problems using FD | Gobbert (SISC) |
| 15 | Mo 10/25 | Review of basic numerical methods for ODEs and their convergence theory | Ascher & Petzold |
| 16, #5 | We 10/27 | Linear stability theory for ODE methods and the concept of stiffness | Ascher & Petzold |
| 17 | Mo 11/01 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |
| We 11/03 | 12:00-01:00, ENGR 122: CIRC Software workshop: MPI (Message Passing Interface) | ||
| 18 | We 11/03 | The non-linear solver inside implicit ODE methods | Gobbert et al. |
| 19, #6 | Mo 11/08 | Implementation issues and higher dimensional problems | Gobbert (SISC) |
| 20 | We 11/10 | The finite element method for parabolic problems | Gobbert (SISC) |
| 21 | Mo 11/15 | Theory of the finite element method for parabolic problems | Thomée (Ch. 1) |
| 22 | We 11/17 | Parallel computing for non-linear reaction-diffusion equations | Gobbert (SISC) |
| 23, #7 | Mo 11/22 | Theory of hyperbolic partial differential equations | Strikwerda (Sec. 1.1-1.2) |
| 24 | We 11/24 | Finite differences for the scalar transport equation | Strikwerda (Sec. 1.3-1.4) |
| 25 | Mo 11/29 | Theory for FD for the scalar transport equation | Strikwerda (Sec. 1.5-1.6) |
| 26 | We 12/01 | Finite elements for hyperbolic conservation laws | Baumann & Oden |
| 27, #8 | Mo 12/06 | Parallel computing for hyperbolic conservation laws | Gobbert et al. (JSC) |
| 28 | We 12/08 | Other numerical methods for PDEs and review | |
| 29 | Mo 12/13 | Preparation for project presentations | |
| Fr 12/17 | 01:00-03:00 Project Presentations | Note date and time! | |