Class | Date | Main Topic | References |
1 | We 08/29 | Overview: an application example | Gobbert (SISC) |
Mo 09/03 | Labor Day | ||
2, #1 | We 09/05 | Prototype problems for elliptic, parabolic, and hyperbolic PDEs | Evans (Ch. 1 and 2) |
3 | Mo 09/10 | The finite difference method for elliptic problems | Gobbert (Notes) |
4 | We 09/12 | Linear solvers and Matlab programming | |
5 | Mo 09/17 | Idea of the finite element method for elliptic problems | Gockenbach |
We 09/19 | 12:00-01:00, ENGR 122: CIRC Workshop: Advanced Programming in MATLAB | CIRC Tutorial | |
6 | We 09/19 | Weak derivatives and Sobolev spaces | Braess (Sec. II.1) |
7, #2 | Mo 09/24 | The weak form of elliptic PDEs | Braess (Sec. II.2) |
8 | We 09/26 | Galerkin orthogonality and Céa's lemma, standard finite elements | Braess (Sec. II.4, II.5) |
Fr 09/28 | 02:30-03:30, MP 401: Colloquium talk: methods for non-linear reaction-diffusion equations | ||
9 | Mo 10/01 | Approximation theory and convergence of the FEM in the H1- and L2-norms | Braess (Sec. II.6-II.7) |
10, #3 | We 10/03 | Introduction to COMSOL Multiphysics: GUI and scripting | Gobbert (COMSOL) |
11 | Mo 10/08 | Test (FD and FEM for elliptic problems) | |
12 | We 10/10 | Demonstration of the CAD facilities of COMSOL Multiphysics | |
13 | Mo 10/15 | Analysis of FEM convergence in COMSOL Multiphysics | Gobbert (COMSOL) |
14, #4 | We 10/17 | The method of lines for a parabolic prototype problems using FD | Yang & Gobbert (Tech. Rep.) |
15 | Mo 10/22 | Review of basic numerical methods for ODEs and their convergence theory | Ascher & Petzold |
16, #5 | We 10/24 | Linear stability theory for ODE methods and the concept of stiffness | Ascher & Petzold |
17 | Mo 10/29 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |
18 | We 10/31 | The non-linear solver inside implicit ODE methods | Gobbert et al. (SISC) |
19, #6 | Mo 11/05 | Implementation issues and higher dimensional problems | Gobbert et al. (SISC) |
20 | We 11/07 | The finite element method for parabolic problems | Gobbert (SISC) |
21 | Mo 11/12 | Theory of the finite element method for parabolic problems | Thomée (Ch. 1) |
22 | We 11/14 | Parallel computing for non-linear reaction-diffusion equations | Gobbert (SISC) |
23, #7 | Mo 11/19 | Theory of hyperbolic partial differential equations | Strikwerda (Sec. 1.1-1.2) |
24 | We 11/21 | Finite differences for the scalar transport equation | Strikwerda (Sec. 1.3-1.4) |
25 | Mo 11/26 | Theory for FD for the scalar transport equation | Strikwerda (Sec. 1.5-1.6) |
26 | We 11/28 | Finite elements for hyperbolic conservation laws | Baumann & Oden |
27, #8 | Mo 12/03 | Parallel computing for hyperbolic conservation laws | Gobbert et al. (JSC) |
28 | We 12/05 | Other numerical methods for PDEs and review | |
29 | Mo 12/10 | Preparation for project presentations | |
Fr 12/14 | 02:30 p.m. Project Presentations | Note date and time! | |