Lecturer:
Course Type:
PhD Course
Academic Year:
2016-2017
Duration:
20 h
Description:
An advanced course dedicate to the analysis of finite element methods, as found in modern numerical analysis literature. A basic knowledge of Sobolev spaces is expected.
Detailed program
Review of basic results for Finite Element Analysis (Galerkin method) (2h)
- Lax Milgram Lemma
- Cea’s Lemma
- Bramble Hilbert Lemma
- Inverse estimates
- Trace estimates
Non-conforming finite element methods (2h)
- Strangs I and II Lemmas
- Symmetric Interior Penalty method
- Analysis of SIP DGFEM
Mixed and hybrid finite element methods (4h)
- Mixed Laplace Problem
- Stokes Problem
- A priori error estimates (exploiting Strang Lemmas)
- Proving the inf-sup (Fortin’s trick, macroelement technique)
Fluid structure interaction problems (2h)
- Problem definition
- Classical Finite Element Approximation: Arbitrary Lagrangian Eulerian Formulation
Immersed Boundary Method (2h)
- Definition
- Finite Difference Approximation
- Dirac Delta Approximation
Immersed Finite Element Method (4h)
- Definition
- Analysis of IFEM - 1D simple case
- Stability of IFEM (2D and 3D case)
Student projects (4h)
- Short seminars from students, valid as exam
Research Group:
Location:
A-133