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FMVE050: The Mathematical Theory of FEM, Spring 2016

Literature:

S. C. Brenner and L. R. Scott "The Mathematical Theory of Finite Element Methods", 3rd Edition, Springer, 2008.

Course description:

The course covers mathematical aspects of the finite element method, in particular finite elements, polynomial approximation, and error estimation. The first ten lectures will be based on Chapters 0-5 and 9 in the book by Brenner and Scott the last 4-5 will be given by the participants on topics related to the finite element method. There will also be assignments that the participants should hand in during the course. The examination consists of the assignments and the lecture. The course gives 7.5 credits.

Teacher:

Axel Målqvist

Schedule:

Lecture 1, Thu 28/1, MVL15, Chapter 5, Introduction (pdf)
Lecture 2, Fri 29/1, MVL14, Chapter 0, FEM in 1D (pdf)
Lecture 3, Thu 4/2, MVL15, Chapter 1, Sobolev spaces and inequalities (pdf)
Lecture 4, Fri 5/2, MVL14, Chapter 3.1-3.2, The finite element (pdf)
Lecture 5, Thu 11/2, MVL15, Chapter 3.3-3.4, The interpolant (pdf)
Lecture 6, Fri 12/2, MVL14, Chapter 4.1-4.2, Polynomial approximation theory (pdf)
Lecture 7, Thu 18/2, MVL15, Chapter 4.3-4.5, Interpolation error (pdf)
Lecture 8, Fri 19/2, MVL14, Chapter 4.8, The Scott-Zhang interpolant (pdf)
Lecture 9, Thu 25/2, MVL15, Chapter 9.1-9.3, Error estimation (pdf)
Lecture 10, Fri 26/2, MVL15, CANCELLED
Lecture 11, Thu 3/3, MVL15, Semi-linear parabolic (Anna) and Stokes (Carl)
Lecture 12, Fri 4/3, MVL15, Linear elasticity (Lars) and (Gustav)
Lecture 13, Thu 10/3, MVL15, Maxwell (John) and Schrodinger (Christoffer)
Lecture 14, Fri 11/3, MVL14, Stochastic FEM (Andreas), Convection-diffusion (Anders), and Shallow water (Tim)
Lecture 10, Thu 17/3, MVL15, Chapter 9.5, A convergent adaptive algorithm (pdf)
I encourage the participants to show numerical simulations in their lectures and I suggest the FEniCS software to be used.

Exercises:

Problems 5.x.12, 0.x.6, 0.x.10, 1.x.13, 3.x.3, 3.x.10, 4.x.9, 4.x.10, 9.x.5, (9.x.10), hand in by the end of February.