Bachelor and Master theses in numerical analysis

Jun.-Prof. Dr. Mira Schedensack
Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut

Bachelor or Master theses in numerical analysis typically consist of a theoretical and a practical part. In the practical part, the candidate is expected to implement an algorithm and test it in numerical experiments. The evaluation of the numerical experients includes a description of the results obtained, a comparison the theoretical results, and, depending on the topic, comparisons with other algorithms, for example.

Prerequisites for a thesis in numerical analysis are an interest in numerical topics. A bachelor thesis is typically based on the lecture "Numerical Analysis of Differential Equations" For a master thesis, students should also have taken at least one, prefarably more advanced courses.

If you are interested in writing a thesis in numerical analysis, we suggest that you contact the possible advisor early. Topics will then be assigned on an individual basis depending on the lectures you have attended.

topics already assigned

• A Kačanov iteration for the Bingham problem (Bachelor thesis)
• A posteriori error estimates for a singularly perturbed reaction diffusion problem (Bachelor thesis)
• Companion operators for the higher-order Crouzeix-Raviart FEM for diffusion reaction problems (Diploma thesis)
• Medius Analysis for a discontinuous Galerkin FEM for linear elasticity (Diploma thesis)
• Numerical analysis of a semilinear elliptic PDE with critical exponent (Diploma thesis)
• A posteriori estimates for a nonconforming approximation for the p-Laplacian (Diploma thesis)
• Adaptive mesh-refinement for the convection dominated convection diffusion equation (Diploma thesis)
• Adaptivity for the Localized Orthogonal Decomposition (Diploma thesis)
• A quantum realization of a finite element method (Bachelor thesis)
• A non-conforming variant of the Localized Orthogonal Decomposition for multiscale problems (Diploma thesis)