Lecturer:
Course Type:
PhD Course
Academic Year:
2019-2020
Period:
March - May
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 programA priori estimates
- Lax Milgram Lemma
- Cea’s Lemma
- Bramble Hilbert Lemma
- Inverse estimates
- Trace estimates
Stabilization mechanisms
- Diffusion-Transport-Reaction equations
- Strongly consistent stabilizations (Galerkin Least Square (GLS), and Streamline Upwind Petrov Galerkin (SUPG) methods)
Mesh adaptivity and a posteriori estimates
- a posteriori error estimates
- solve, estimate, mark, refine
Non-conforming finite element methods
- Strangs I and II Lemmas
- Symmetric Interior Penalty method
- Analysis of SIP DGFEM
Mixed and hybrid finite element methods
- Mixed Laplace Problem
- Stokes Problem
- A priori error estimates (exploiting Strang Lemmas)
- Proving the inf-sup (Fortin’s trick, macroelement technique)
Non matching discretisation techniques
- Immersed Boundary Method
- Dirac Delta Approximation
- Immersed Finite Element Method
Short seminars from students, valid as exam
Research Group:
Location:
Zoom (sign in to get password)