Variational Inequalities

Moodle, LSF

Yousept, Renner, Matos de Souza

1. Theory of variational inequalities of first and second kind

2. Examples of variational inequalities in Sobolev spaces

3. Convex analysis and Fenchel duality

4. Semismooth Newton method

 1. Trémolières,  Lions, Glowinski - Link

2. Kinderlehrer, Stampacchia - Link

Master Seminar on Wave Phenomena

LSF

Practical Implementation of Numerical Methods

Moodle, LSF

Acoustic and Electromagnetic Wave Phenomena

Moodle, LSF

Yousept, Ammann

1. Normal Trace and Tagential Trace Operator

2. Helmholtz Decomposition

3. Magnetostatics and Maxwell's Equations

4. Evolution Equations and Semigroup Theory

Master Seminar on Optimal Control

LSF

Practical Implementation of Optimization Methods

Moodle, LSF

Optimal Control of PDEs

Moodle, LSF

Yousept, Ammann

1. Introduction to Sobolev Spaces

2. Weak Solutions to Elliptic Equations

3. Linear-Quadratic Elliptic Control Problems

4. Optimal Control of Semilinear Elliptic Equations

1. Tröltzsch - Link

Master Seminar on Variational Inequalities

LSF

Practical Implementation of Optimization Methods

Moodle, LSF

Numerical Methods for Variational Inequalities

Moodle, LSF

Yousept, Ammann

1. Theory of variational inequalities of first and second kind

2. Examples of variational inequalities in Sobolev spaces

3. Convex analysis and Fenchel duality

4. Semismooth Newton method

1. Trémolières,  Lions, Glowinski - Link

2. Kinderlehrer, Stampacchia - Link

Practical Implementation of Optimization Methods

Moodle, LSF

Yousept, Ammann

Analysis and Implementation of Certain Optimization Methods

Introduction to Numerical Methods

Moodle, LSF

1. Interpolation and Numerical Integration

2. Direct and Indirect Solvers for Linear Systems

Inverse Problems

Moodle, LSF

Yousept, Ammann

1. Introduction to inverse problems

2. Selected topics from functional analysis

3. Linear inverse problems

4. Regularization methods

5. Convergence rates

1. Hofmann - Link

2. Kirsch - Link

Practical Implementation of Numerical Methods

Moodle, LSF

Yousept, Ammann

Analysis and Implementation of Certain Numerical Methods

1. Nocedal, Wright - Link

Introduction to Numerical Methods

Moodle, LSF

Hensel, Ammann

1. Interpolation and Numerical Integration

2. Direct and Indirect Solvers for Linear Systems

3. Iterative Methods for Nonlinear Systems

1. Stoer, Bulirsch - Link

Master Seminar on Optimal Control

LSF

Practical Implementation of Optimization Methods

Moodle, LSF

Yousept, Ammann

Analysis and Implementation of Certain Optimization Methods

1. Nocedal, Wright - Link

Optimal Control of PDEs

Moodle

Yousept, Hensel

1. Introduction to Sobolev Spaces

2. Weak Solutions to Elliptic Equations

3. Linear-Quadratic Elliptic Control Problems

4. Optimal Control of Semilinear Elliptic Equations

1. Tröltzsch - Link

Master Seminar on Numerical Analysis

LSF

Advanced Numerical Methods

Moodle

Hensel, Ammann

1. Numerical Analysis of ODEs

2. Basic Notions of the Variational Framework for PDEs

3. Finite Element Method

1. Evans - Link

2. Ciarlet - Link

Numerical Analysis of PDEs

Moodle

1. Introduction to Sobolev Spaces

2. Weak Solutions to Elliptic Equations

3. Finite Element Method for Linear Elliptic PDEs and Error Estimates

1. Adams - Link 

2. Wloka - Link

3. Evans - Link

4. Grisvard - Link

5. Ciarlet - Link

Bachelor Seminar on Numerical Analysis

LSF

Practical Implementation of Numerical Algorithms

LSF

Analysis and Implementation of Certain Numerical Algorithms from Previous Lectures

Introduction to Numerical Methods

Moodle

Winckler, Ammann

1. Interpolation and Numerical Integration

2. Direct and Indirect Solvers for Linear Systems

3. Iterative Methods for Nonlinear Systems

1. Stoer, Bulirsch - Link