Math 621 - Numerical Methods for Partial Differential Equations

Spring 2017 - Matthias K. Gobbert

Detailed Schedule - Last Updated 04/11/17

This schedule is designed to give you an overview of the material to be covered and is tentative in nature. This is a living document and will be updated throughout the semester.
The entries in the column References point to a number of standard references in the field. See my webpage on recommended literature for the complete citations.
The numbers #0, #1, #2, etc. in the Class column indicated that the homework with that number is due at the beginning of class that day.
The color coding classifies the topic of the material, with green and blue colors for material on the finite difference and the finite element methods, respectively, the actual contents of the course. But to apply either of these methods, we need tools including linear solvers, non-linear solvers, and ODE solvers, color-coded in red.
The orange color indicates software workshops on Matlab, offered by the Center for Interdisciplinary Research and Consulting (circ.umbc.edu)

Class	Date	Main Topic	References
1	Tu 01/31	Overview: Math 621 in a nutshell	Gobbert (2008)
2, #0	Th 02/02	Prototype problems for elliptic, parabolic, and hyperbolic PDEs	Evans (Ch. 1 and 2)
3, #1	Tu 02/07	The finite difference method for elliptic problems	HPCF-2017-3
	We 02/08	12:00-01:00, ENGR 122: CIRC Software workshop: Basic MATLAB
4	Th 02/09	Convergence Theory for FD for elliptic problems	Gobbert (Notes)
5	Tu 02/14	Linear solvers and Matlab programming: CG and preconditioning	Allen (2004)
6	Th 02/16	The method of lines for a parabolic prototype problem using FD	Gobbert (slides)
7	Fr 02/17	Implementation issues and higher dimensional problems; make-up for 02/28/17	Gobbert (Notes)
8, #2	Tu 02/21	Implementation issues of MOL-FD for non-linear systems of PDEs	Gobbert (slides)
	We 02/22	12:00-01:00, ENGR 122: CIRC Software workshop: Basic Programming in MATLAB
9, #3	Th 02/23	Numerical methods for stiff systems of ODEs	Shampine & Reichelt
	Tu 02/28	Class cancelled; make-up was 02/17/17
10	Th 03/02	Library Training Session in room LIBR 259
11	Tu 03/07	Derivation of BDFk and NDFk, Newton method, linear solver	Gobbert (slides)
	We 03/08	12:00-01:00, ENGR 122: CIRC Software workshop: Intermediate Programming in MATLAB
12	Th 03/09	Numerical methods for stiff systems of ODEs	Shampine & Reichelt
13	Tu 03/14	Snow cancellation
14, #4	Th 03/16	Matlab implementation of NDFk and PCG
	Tu 03/21	Spring Break
	Th 03/23	Spring Break
15	Tu 03/28	Idea of the finite element method for elliptic problems	Braess (Sec. II.7)
	We 03/29	12:00-01:00, ENGR 122: CIRC Software workshop: Advanced Programming in MATLAB
16, #5	Th 03/30	Weak derivatives and Sobolev spaces	Braess (Sec. II.1)
17	Tu 04/04	The weak form of elliptic PDEs	Braess (Sec. II.2)
18, #6	Th 04/06	Definition of a FEM solution from the discrete weak form	Braess (Sec. II.8)
19	Tu 04/11	Abstract formulation of weak with bilinear form	Braess (Sec. II.2)
20, #7	Th 04/13	Galerkin orthogonality and Céa's lemma	Braess (Sec. II.4)
21, #8	Tu 04/18	Standard finite elements	Braess (Sec. II.5)
22	Th 04/20	The finite element method for parabolic problems	Gobbert (slides)
23, #9	Tu 04/25	Theory of the finite element method for parabolic problems	Thomée (Ch. 1)
24	Th 04/27	Introduction to hyperbolic partial differential equations	Strikwerda (Sec. 1.1-1.2)
25	Tu 05/02	Finite differences for the scalar transport equation	Strikwerda (Sec. 1.3-1.4)
26	Th 05/04	Theory for FD for the scalar transport equation	Strikwerda (Sec. 1.5-1.6)
27, #10	Tu 05/09	Finite elements for hyperbolic conservation laws	Baumann & Oden
28	Th 05/11	Other numerical methods (finite volume method) for PDEs and review	Huang et al. (2017)
29	Tu 05/16	Review
	Th 05/18	01:00 p.m. Final exam	Note date and time!