Lecture plan
The following plan is tentative. Changes will occur. As the semester unfolds it will be gradually be updated and by the start of December, it will be considered to be the curriculum.
| Lecture | Topic | Reading | Additional Reading |
|---|---|---|---|
| Week 34 | Introduction to FEM, Poisson 1D, Weak Form, Different boundary conditions | Quarteroni 3.2 | H1 |
| Discretization in 1D, linear hat functions, Galerkin problem and orthogonality | Quarteroni 4.1-4.3 | H2 | |
| Week 35 | Mathematical background: Lebesgue and Sobolev spaces | Sobolev spaces | H1, Quarteroni 2 |
| Lagrange basis functions of degree p, reference element, interpolation error | Quarteroni 4.2-4.3 | H3 | |
| Week 36 | Poisson 2D (theory), mixed boundary conditions, lifting function | Quarteroni 3.2-3.3 | H4 |
| Discretization in 2D (implementation), triangulation | H4 | Quarteroni 4.5 | |
| Week 37 | Numerical integration, gauss quadrature, reference coordinate system | H4 | Quarterioni 8.2 |
| Barycentric coordinates, high order elements | Quarteroni 4.4-4.5 | ||
| Week 38 | Change of variables, integration and derivation | Quartertoni 8.2 | |
| NO LECTURE | - | ||
| Week 39 | Displacement, shear strain, normal strain, tensors | Wikipedia (Strain) | Linear Elasticity, Strains |
| Traction vectors, stress tensor, equilibrium equations | Stresses (2.1-2.8) | Wikipedia (Stress) | |
| Week 40 | General elliptic problems, Linear Elasticity equations | Quarteroni 3.4 | Linear Elasticity |
| Implementing boundary conditions: Big number, explicit elimination, lifting functions | Quarteroni 3.3, H4 (4.5) | ||
| Week 41 | Problem set 2 discussion | Programming Project | |
| Quadrilatheral elements, grid generation in 1D, legal grids | Quarteroni 6.1-6.2 | ||
| Week 42 | Generation of structured and un-structured grids, regularization techniques | Quarteroni 6.2-6.5 | |
| Condition number of stiffness matrices | Quarteroni 4.5 | ||
| Week 43 | Parabolic equations, the \(\theta\)-method | Quarteroni 5.1 | |
| Convergence and stability of the \(\theta\)-method | Quarteroni 5.4-5.5 | ||
| Week 44 | Convergence rates 2D poisson, interpolation error in 2D | Quarteroni 4.5 | |
| A posteriori error estimates | Quarteroni 4.6 | ||
| Week 45 | Solution techniques for linear systems | Quarteroni 7 | |
| Project presentation | - | ||
| Week 46 | Programming, assembly, local element matrices, vectorization, sparse matrices | Quarteroni 8.3-8.4, FEM.zip | |
| Iterative methods, preconditioners, parallelization | Quarteroni 7.2, 8, FEM.zip | ||
| Week 47 | Repetition, old exams | - |