Applied and numerical analysis, optimization
Applied Analysis focuses on the analysis and derivation of mathematical models for processes in
the natural and engineering sciences. Methods from real and functional analysis are applied to
differential equations and variational problems to prove existence and properties of solutions.
The aim is an explanation or better understanding of physical phenomena.
Numerical analysis is the understanding and design of algorithms to compute approximations to mathematical models like differential equations. The numerical analysis group focuses on the a priori and a posteriori discretisation error analysis of a new generation of methods and adaptive algorithms with rate optimality. It includes perturbation analyses and method development for coupled models and a hierarchy of models in various applications.
Mathematical optimization focuses on the development, analysis and implementation of algorithms to systematically determine extreme points of a given function under constraints. For this purpose, problem structures like underlying partial differential equations and special properties such as nonsmoothness of the involved functions are exploited.
- Multidimensional calculus of variations
- Analysis of nonlinear partial differential equations
- Discretizations for partial differential equations
- Numerical analysis for partial and ordinary differential equations with constraints
- Optimization with partial differential equations
- Nonsmooth optimization
- Applications in computational mechanics, energy networks, electronic and photonic devices, material sciences