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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 MålqvistSchedule:Lecture 1, Mon 27/1, 13-15, MVL14, Chapter 5, Introduction (pdf)Lecture 2, Wed 29/1, 10-12, MVL14, Chapter 0, FEM in 1D (pdf) Lecture 3, Mon 3/2, 13-15, MVL14, Chapter 1, Sobolev spaces and inequalities (pdf) Lecture 4, Wed 5/2, 10-12, MVL14, Chapter 3.1-3.2, The finite element (pdf) Lecture 5, Mon 10/2, 13-15, MVL14, Chapter 3.3-3.4, The interpolant (pdf) Lecture 6, Wed 12/2, 10-12, MVL14, Chapter 4.1-4.2, Polynomial approximation theory (pdf) Lecture 7, Mon 17/2, 13-15, MVL14, Chapter 4.3-4.5, Interpolation error (pdf) Lecture 8, Wed 19/2, 10-12, MVL14, Chapter 4.8, The Scott-Zhang interpolant (pdf) Lecture 9, Mon 24/2, 13-15, MVL14, Chapter 9.1-9.3, Error estimation (pdf) Lecture 10, Wed 26/2, 10-12, MVL14, Chapter 9.5, A convergent adaptive algorithm (pdf) Lecture 11, Mon 2/3, 13-15, MVL14, FEM in time (Per) and Elasticity (Morgan) Lecture 12, Wed 4/3, 10-12, MVL14, Variational crimes (Gulshan) and Surface FEM (Erik) Lecture 13, Mon 9/3, 13-15, MVL14, Mixed dimension (Malin) and Multilevel MC (Kasper) 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. |
