Numerical methods for saddle point problems

Summary
The aim of the course is to give a theoretical and practical knowledge of the finite element method for saddle point
problems.
Content
– Minimization of convex functionals (energies) under linear constraints and their interpretation as saddle point problems.
Wellposedness and inf-sup conditions.
– Finite element approximation of saddle point problems, discrete inf-sup conditions, stability and approximation
estimates
– Finite elements for Stokes flows, (quasi-)incompressible linear elasticity, and Darcy flows
– Compatible discretisations of differential forms and of Maxwell equations
Learning Prerequisites
Required courses
Analysis I II III IV, Numerical Analysis, Advanced numerical analysis, Sobolev spaces and elliptic equations.
Recommended courses
Functional analysis I, measure and integration, Programming
Bibliography
– D. Boffi, F. Brezzi, M. Fortin Mixed Finite Element Methods and Applications, Springer Series in
Computatioanl mathematics, 2013.
– P. Monk, Finite Element Methods for Maxwell Equations, Oxford University press, 2003
– A. Ern, J-L. Guermond, Theory and Practise of Finite Elements, Springer 2004.