Two PhD Positions in Numerical Analysis
Functional A Posteriori Estimates for Modeling Errors
The simulation of complicated physcial phenomena consists of several steps which includes the mathematical modeling and the numerical discretization. For the reliability of the solutions, it is of utmost importance to estimate the modeling and numerical errors in an a posteriori way. While the a posteriori control of the numerical discretization error has been developed since the 1980s, the control of the modeling error is still in its infancies and a topic of vivid worldwide research in Numerical Analysis. The recent development of a "functional error majorant" for Poisson-type problems is a first milestone in this direction and its generalization to new problem classes is the topic of these PhD-Projects.
In this project, the functional a posteriori error majorant should be developed for two kinds of important applications:
Project A: A posteriori error estimation for the modeling error arising if thin elastic structures as they, e.g., appear in cooling towers, are replaced by two-dimensional models.
Project B: A posteriori error estimation for the modeling error arising if periodic structures as they, e.g., appear in design of composite materials, are modeled as homogenized problems.
In both projects the goal is to derive the functional error majorant and the development of an algorithm which is adaptive with respect to both: the numerical and the modeling error.
3) Prerequisites: Master in mathematics, preferable in one or more of the fields: numerical analysis/applied analysis/computational mathematics/partial differential equations.
4) Conditions/Applications: These projects are funded by the Swiss National Science Foundation.
The I-Math at the University of Zurich provides an excellent environment and infrastructure for their PhD students. PhD students are members of the Zurich Graduate School in Mathematics (ZGSM) which is jointly run with the D-Math at the ETH Zurich. Both PhD students will be integrated in the
Numerical Analysis/Computational Mathematics research group of Professor Stefan Sauter.
Applications should include electronic versions of your transcripts and, if available, a certificate of the master degree. In addition 3 letters of recommendation are requested.
The application should be send to the head of the Numerical Analysis Group, Professor Stefan Sauter