Omfattning: 5
Tidtabel: 18.04.2019 - 23.05.2019
Kontaktuppgifter till kursens personal (gäller denna kursomgång):
Prof. Rolf Stenberg and Prof. Juha Videman
Närmare beskrivning av kursens innehåll (gäller denna kursomgång):
This is a second course in the finite element method. The topics covered are a posteriori error analysis and a adaptive methods, and problems that are described as minimisation problems subject to constraints.
The content of the course is the following.
Boundary value problems and the FEM
Scalar elliptic equations. Elastic membrane, electromagnetic field, stationary heat conduction.
Vector valued problems. The Navier-Stokes and the Stokes problem. Linear elasticity.
A posteriori error analysis
The Clément interpolation operator. A posteriori estimates. Reliability and efficiency.
Saddle point problems
Babuska’s method of Lagrange multiplier. The Stokes problem. The uniqueness of the continuous and discrete problem. The stability condition and the error in the finite element methods. Examples of FE methods.
Stabilized methods for the Stokes problem
A priori and a posteriori error analysis.
Stabilization of Babuska’s method. Nitsche’s method
Relationship between the methods. Error analysis. Mortaring in domain decomposition.
Variational inequalities
The membrane obstacle problem. Mixed and stabilized finite element methods. Nitsche’s method. The elastic contact problem.
Kursens webbplats (är i kraft 01.08.2018-31.07.2020):
https://mycourses.aalto.fi/course/search.php?search=MS-E1999
Bedömningsskala (är i kraft 01.08.2018-31.07.2020):
0-5
Tilläggsinformation (är i kraft 01.08.2018-31.07.2020):
Content varies.