Class Notes
M1 Mathematics, 2011-2012
MM26E Numerical Approximation of PDEs

Hervé Le Dret


These notes describe the material that will be covered in class, except for the first chapter due to the first three classes missed. I will post the chapters based on the progression in class.

Just in case, here is a link to notes of a M1 class I taught in the past, that include more detail on such basic tools in analysis as convolution, distributions and so on: Outils de base en analyse appliquée. These notes are in French.



Chapters

Chapter 1. Mathematical modeling and PDEs. 31 pages, 569 kB.

Chapter 2. A review of analysis. 41 pages, 5.8 MB.

Chapter 3. The variational formulation of elliptic PDEs. 28 pages, 369 kB.

Chapter 4. Variational approximation methods for elliptic PDEs. 20 pages, 344 kB.

Chapter 5, part 1. The finite element method in dimension 2. Rectangular elements, 30 pages, 2.7 MB.

Chapter 5, part 2. The finite element method in dimension 2. Triangular elements, 14 pages, 1.2 MB.

Chapter 6, part 1. The heat equation. Theoretical study, 32 pages, 3.8 MB. For cultural purposes only, essentially skipped in class due to lack of time.

Chapter 6, part 2. The heat equation. Finite difference schemes, 33 pages, 2.4 MB.



Illustrations about finite elements

Click here for a few images pertaining to $Q_1$-Lagrange rectangular finite elements.

Click here for a few images pertaining to $Q_2$-Lagrange rectangular finite elements.

Click here for a few images pertaining to $Q_3$-Hermite rectangular finite elements.

Click here for a few images pertaining to $P_1$-Lagrange triangular finite elements.

Click here for a few images pertaining to $P_2$-Lagrange triangular finite elements.

Click here for a few images pertaining to $P_3$-Lagrange triangular finite elements.



Animations about finite difference methods

Click here for an animation of the backward Euler scheme.

Click here for an animation of the forward Euler scheme.

Click here for an animation of the leapfrog scheme.



Final exam May 2012.
Quick and dirty correction.

Last updated: May 24, 2012.



This class was the source of a book with B. Lucquin, Partial Differential Equations: Modeling, Analysis, and Numerical Approximation, with a lot more content.