MATH 661



Class: TR 14:20-15:35, Bloc160
Prof: Jean-Luc Guermond

First Day Handout

Lectures notes: (To be posted)

Lecture notes will be posted in advance. You have to read them IN ADVANCE and do as many exercises as possible. The material of the lecture notes will be reviewed in class ASSUMING that you have read the lecture notes in advance.

FE approximation theory, Week1 to Week 6 (Appendices A and B + references)

Week1, Chap01 (Lebesgue integration), Chap02 (Sobolev spaces), Chap03 (Trace theory, Poincare-Steklov ineq.), (Further reading Chap04) (A little bit of funcional analysis)
Week2, Chap05 (Elementary notions on FE, Ciarlet triple), (Further reading Chap06 (Tensor product FE)),
Week3, Chap07 (Simplicial FE), (Further reading Chap08 (Meshes)), Chap09 (FE generation and diff calculus),
Week4,  Chap10 (Mesh orientation), Chap11 (Local interpolation), (Further reading Chap 12 (Local inverse ineq.))
Week5, Chap 14 (Hdiv FE), Chap 15 (Hcurl FE)
Week6, Chap16 (Hdiv and Hcurl approximation), (mandatory reading Chap18 before Chap19, broken FE spaces), Chap19 (Conforming FE spaces), (Futher reading, Chap20, Chap21)

PDE approximation Week 7 until the end of the semester (recommended reading: Appendix C + references)

Week7, Chap 24 (Weak formulations) + Chap25 (Wellposedness, BNB),  Chap26  (Galerkin approx)
Week8, Chap27 (Variational crimes),   Chap 35 (Helmholtz),
Week9,  Chap 36 (Crouzeix Raviart), Chap 37 (Nietche's method),
Week10, Chap38 (dG), (Chapter 46 mandatory reading in preparation for Chap 47 and 48), Chap 47 (symmetric eigenvalue problems),
Week11, Chap 48 (nonsymmetric eigenvalue problems), Chap43 (Maxwell, conforming Hcurl approx),
Week12, Chap44 (Maxwell with divergence control), Chap49 Mixed problems,
Week13, Chap50 (Mixed approximation),
Week13, Chap53 (Stokes), Chap54 (Stokes), Chap55 (Stokes),

Mid Term:

Final: